Rotational kinetic energy and conservation of energy was the order of the day for B, C and F Blocks. Rotational kinetic energy is another form of mechanical energy and should rightfully be included when considering conservation of energy. When working problems, remember the tips that we discussed in class and just be very careful and systematic when setting up your equations. Tomorrow, we begin a discussion of simple machines, mechanical advantage and efficiency...
...which was what E Block investigated in lab today. You worked with levers and pulleys, two machines that rely on torque to function, and analyzed how repositioning the effort force for levers and changing number of supporting ropes for pulleys affected mechanical advantage. Effectively, how did changing distance affect the amount of force needed to raise your load or resistance. Machines cannot give us more work out than we put in, but they can increase our effort force or distance. If effort force is increased, the force acts over a small distance. If effort distance is increased, it only generates a small output force. Both factors cannot be multiplied simultaneously. We'll discuss the lab tomorrow and begin our discussion of simple machines, using your results to highlight our talk.
11/30/11
11/29/11
Rotational Analogues
More of those on deck today for B, C and E Blocks. B Block went over their work on rotational equilibrium, Newton's nd Law for rotation and angular momentum. Tomorrow, we'll add on rotational kinetic energy and start our examination of simple machines.
C Block covered the same ground as B Block, but added on rotational kinetic energy, to boot. Rotational kinetic energy is another form of mechanical energy and rotating objects can have plain ol' kinetic energy, rotational kinetic energy or both, depending on the circumstances. Remember to choose shapes wisely for calculating moment of inertia for objects and that vt and ω can be interchanged using the relationship we learned last chapter:
vt = rω
Problems often ask you to solve for something like the translational speed of an object after it has rolled down a ramp and you have to use conservation of energy to do so. Rewriting the rotational kinetic energy formula in terms of translational velocity (KErot = 1/2 I(vt2/r2)reduces the number of velocity variables in the problem to one - the one for which you want to solve. You can also rewrite translational kinetic energy in terms of angular speed, if that is the speed you are asked to determine: KE = 1/2 m(rω)2). And, problems can go the other way - giving you a speed, mass and radius and asking how high something would roll up a ramp. You'd have to use that one speed in both kinetic energy formulas so that you could determine the final gravitational potential energy and, therefore height. Tomorrow, we go over these ideas and then move on to simple machines.
E Block got all three new descriptors of rotational motion in one blast and were left having to analyze conservation of angular motion and rotational kinetic energy for a demonstration. We'll go over that tomorrow before you begin your lab work on simple machines.
F Block conducted a lab investigation on torque and rotational equilibrium. As we had discussed in lab, balance (rotational equilibrium) is based on an absence of net torque not an absence of net force and you demonstrated that quite nicely today. You had unequal forces on either side of the meter stick, but by positioning them at the proper locations, you were able to achieve equilibrium. We'll go over the lab tomorrow before moving on to rotational kinetic energy and conservation of energy for rotating systems.
C Block covered the same ground as B Block, but added on rotational kinetic energy, to boot. Rotational kinetic energy is another form of mechanical energy and rotating objects can have plain ol' kinetic energy, rotational kinetic energy or both, depending on the circumstances. Remember to choose shapes wisely for calculating moment of inertia for objects and that vt and ω can be interchanged using the relationship we learned last chapter:
Problems often ask you to solve for something like the translational speed of an object after it has rolled down a ramp and you have to use conservation of energy to do so. Rewriting the rotational kinetic energy formula in terms of translational velocity (KErot = 1/2 I(vt2/r2)reduces the number of velocity variables in the problem to one - the one for which you want to solve. You can also rewrite translational kinetic energy in terms of angular speed, if that is the speed you are asked to determine: KE = 1/2 m(rω)2). And, problems can go the other way - giving you a speed, mass and radius and asking how high something would roll up a ramp. You'd have to use that one speed in both kinetic energy formulas so that you could determine the final gravitational potential energy and, therefore height. Tomorrow, we go over these ideas and then move on to simple machines.
E Block got all three new descriptors of rotational motion in one blast and were left having to analyze conservation of angular motion and rotational kinetic energy for a demonstration. We'll go over that tomorrow before you begin your lab work on simple machines.
F Block conducted a lab investigation on torque and rotational equilibrium. As we had discussed in lab, balance (rotational equilibrium) is based on an absence of net torque not an absence of net force and you demonstrated that quite nicely today. You had unequal forces on either side of the meter stick, but by positioning them at the proper locations, you were able to achieve equilibrium. We'll go over the lab tomorrow before moving on to rotational kinetic energy and conservation of energy for rotating systems.
11/28/11
Turkey in the Rear-View Mirror
Back to Work!
B, C and F Blocks reviewed the concepts of torque, center of mass, moment of inertia and rotational equilibrium before moving on to Newton's 2nd Law for rotational motion and angular momentum. When working with N-2 for rotation, the relationships between the variables are the same as for plain ol' vanilla N-2. Net torque is directly proportional to angular acceleration and inversely proportional to moment of inertia:
τnet = Iα
For angular momentum, again, the concept is analogous to translational momentum and the formula is a one-for-one substitution when scripting an expression for angular momentum:
L = Iω
And, yes, angular momentum is conserved in the absence of external torque and we discussed the example of the ice skater going into a spin by bringing in their arms to lower their moment of inertia (to raise angular speed) and also collected data using the rotary motion sensor to verify that conservation of angular moment is a valid idea.
E Block discussed the concept of rotational equilibrium. Extended objects can be analyzed in terms of translation and/or rotational equilibrium and we examined some problems that used both conditions of equilibrium to assess the magnitude of forces acting on systems. We'll go over these problems tomorrow before moving on to Newton's 2nd Law for rotational motion and angular momentum.
B, C and F Blocks reviewed the concepts of torque, center of mass, moment of inertia and rotational equilibrium before moving on to Newton's 2nd Law for rotational motion and angular momentum. When working with N-2 for rotation, the relationships between the variables are the same as for plain ol' vanilla N-2. Net torque is directly proportional to angular acceleration and inversely proportional to moment of inertia:
For angular momentum, again, the concept is analogous to translational momentum and the formula is a one-for-one substitution when scripting an expression for angular momentum:
And, yes, angular momentum is conserved in the absence of external torque and we discussed the example of the ice skater going into a spin by bringing in their arms to lower their moment of inertia (to raise angular speed) and also collected data using the rotary motion sensor to verify that conservation of angular moment is a valid idea.
E Block discussed the concept of rotational equilibrium. Extended objects can be analyzed in terms of translation and/or rotational equilibrium and we examined some problems that used both conditions of equilibrium to assess the magnitude of forces acting on systems. We'll go over these problems tomorrow before moving on to Newton's 2nd Law for rotational motion and angular momentum.
11/27/11
11/23/11
And... We're Done
Well, I am at least. The last two blocks today are my preparation blocks, so I am puttering around the room cleaning up from this week's rotational dynamics labs. B Block finished their data analysis today and we'll discuss what you found on Monday to help you get some ideas for your write-up, although you should already have some idea of what patterns you should be seeing and thinking of reasons why those patterns were wonky, if that happened. C Block discussed rotational equilibrium, which built on the torque and balance lab that we conducted. We looked over a typical problem for rotational equilibrium dealing and students had the chance to practice solving this type of problem. We'll pick up with this when we get back from break.
11/22/11
Facing a Half-Day
Today was the last full day of the week and it was a busy one...
B Block began their rotational motion lab. Data was collected that allowed students to measure angular acceleration for a variety of torques and that information will be plotted to assess the object's moment of inertia. For the rod with weights, we'll also take a look at how changing the spacing of the weights affects the moment of inertia, though from our previous discussions, you should have a pretty good idea as to the outcome. Tomorrow is set aside for graphing and analyzing your data - don't forget to get the rod data from the other groups!
C Block engaged in a discussion of center of mass and moment on inertia, two very important concepts for rotational motion. An object's center of mass is the point around which the object will naturally rotate when acted on only by gravity. It is also the balance point, and if your center of mass moves beyond your base of support - consider yourself toppled. We'll expand on these ideas tomorrow, along with our lab work on torque and balance.
E Block took a look at torque, center of mass and moment of inertia. Torque and moment of inertia are critical in providing a framework around which to evaluate and explain your experimental results from your rotational dynamics lab, so I hoped good attention was paid by all attendees. Remember that your lab is not due until next Tuesday or Wednesday, so don't kill yourself trying to get it written up over the break. But, do start thinking about how the increasing torques affected angular acceleration for each trial, how increasing mass for your discs affected angular acceleration (when subject to the same torque) and how using a different shape played into the game. For your rod, it approximates point masses acting away from the axis of rotation, so you should have some idea of how its moment of inertia should compare with comparably massed discs. Also, how did changing the mass spacing affect the moment of inertia? Did the pattern make sense? If now, explain what might have happened to give unexpected results.
F Block worked on rotational equilibrium - where objects are subject to a net torque of 0. Whether you are not rotating or rotating at constant angular speed, you are in rotational equilibrium - angular acceleration is noted when you are subject to net torque. Objects can exist in translational or rotational equilibrium, both at the same time or neither, depending on the situation. We looked at some problems to see how to use these two conditions of equilibrium to analyze forces in a system. We'll go over them on Monday when we return and see how folks feel about moving on to angular momentum.
If I don't see you tomorrow - have a great Thanksgiving!
B Block began their rotational motion lab. Data was collected that allowed students to measure angular acceleration for a variety of torques and that information will be plotted to assess the object's moment of inertia. For the rod with weights, we'll also take a look at how changing the spacing of the weights affects the moment of inertia, though from our previous discussions, you should have a pretty good idea as to the outcome. Tomorrow is set aside for graphing and analyzing your data - don't forget to get the rod data from the other groups!
C Block engaged in a discussion of center of mass and moment on inertia, two very important concepts for rotational motion. An object's center of mass is the point around which the object will naturally rotate when acted on only by gravity. It is also the balance point, and if your center of mass moves beyond your base of support - consider yourself toppled. We'll expand on these ideas tomorrow, along with our lab work on torque and balance.
E Block took a look at torque, center of mass and moment of inertia. Torque and moment of inertia are critical in providing a framework around which to evaluate and explain your experimental results from your rotational dynamics lab, so I hoped good attention was paid by all attendees. Remember that your lab is not due until next Tuesday or Wednesday, so don't kill yourself trying to get it written up over the break. But, do start thinking about how the increasing torques affected angular acceleration for each trial, how increasing mass for your discs affected angular acceleration (when subject to the same torque) and how using a different shape played into the game. For your rod, it approximates point masses acting away from the axis of rotation, so you should have some idea of how its moment of inertia should compare with comparably massed discs. Also, how did changing the mass spacing affect the moment of inertia? Did the pattern make sense? If now, explain what might have happened to give unexpected results.
F Block worked on rotational equilibrium - where objects are subject to a net torque of 0. Whether you are not rotating or rotating at constant angular speed, you are in rotational equilibrium - angular acceleration is noted when you are subject to net torque. Objects can exist in translational or rotational equilibrium, both at the same time or neither, depending on the situation. We looked at some problems to see how to use these two conditions of equilibrium to analyze forces in a system. We'll go over them on Monday when we return and see how folks feel about moving on to angular momentum.
If I don't see you tomorrow - have a great Thanksgiving!
11/21/11
Rotatin'
B Block took time to focus on the problem solving aspect of rotational equilibrium. Objects can exist in rotational equilibrium, translational equilibrium, neither or both, depending on the specific circumstances. The problems we are looking at have objects in both forms of equilibrium and we are assessing the forces at work. Remember to use both conditions for equilibrium as tools (Fnet = 0 and τnet = 0) and choose rotational axes wisely. A force applied directly to the axis of rotation does not produce torque and that can help reduce the number of variables in a problem. Over the next couple of days, we'll be working on your rotational dynamics lab and I can help you with any individual issues working these problems during lab time.
C Block worked on a lab dealing with torque and balance. When we speak of balance, we are usually talking about an object being in rotational equilibrium and for that to occur, the sum of all torques on the object must be zero. For each mass you placed on your suspended meter stick, you used the weight and lever-arm distance to calculate its individual torque and with a thought about direction, demonstrated that the clockwise torque in your system balanced the counterclockwise torque. The post-lab problems deal with torque and balance and we'll go over those tomorrow before looking at the concepts of center of mass and moment of inertial.
E Block finished the data analysis for their rotational dynamics lab and folks should think carefully about the write-up hints I put on the board. With the disks, how did torque affect angular acceleration and why was the acceleration different between the single disk and the two disks stacked? Why was the slope of the line for your masses on a rod as large a value as it was? Why did the different positions of the masses on the rod affect the slopes of the lines? We'll start going over these ideas in class tomorrow, so pay attention and use those discussions to help script your synopsis.
F Block discussed the idea of center of mass and moment of inertia. We looked at some demonstrations that showed how the ease of rotation was affected by an object's mass distribution and how moment of inertia, torque and angular acceleration played together through the formula τnet = Iα. We'll delve more deeply into that relationship in the next section when we really focus on the role moment of inertia plays in other aspects of rotational motion.
C Block worked on a lab dealing with torque and balance. When we speak of balance, we are usually talking about an object being in rotational equilibrium and for that to occur, the sum of all torques on the object must be zero. For each mass you placed on your suspended meter stick, you used the weight and lever-arm distance to calculate its individual torque and with a thought about direction, demonstrated that the clockwise torque in your system balanced the counterclockwise torque. The post-lab problems deal with torque and balance and we'll go over those tomorrow before looking at the concepts of center of mass and moment of inertial.
E Block finished the data analysis for their rotational dynamics lab and folks should think carefully about the write-up hints I put on the board. With the disks, how did torque affect angular acceleration and why was the acceleration different between the single disk and the two disks stacked? Why was the slope of the line for your masses on a rod as large a value as it was? Why did the different positions of the masses on the rod affect the slopes of the lines? We'll start going over these ideas in class tomorrow, so pay attention and use those discussions to help script your synopsis.
F Block discussed the idea of center of mass and moment of inertia. We looked at some demonstrations that showed how the ease of rotation was affected by an object's mass distribution and how moment of inertia, torque and angular acceleration played together through the formula τnet = Iα. We'll delve more deeply into that relationship in the next section when we really focus on the role moment of inertia plays in other aspects of rotational motion.
11/18/11
600!
This is the 600th Index of Refraction blog post - cool...
B and F Blocks began their work with rotational dynamics with a study of torque. Remember that torque is not a force - it is the ability of a force to produce rotation. We looked at some examples of how lever arm affects what the force accomplishes when applied to a rotating body. And don't forget angle - only the component of the force that is perpendicular to the rotation contributes to torque and the formula:
τ = Fd(sinΘ)
takes those factors into account. We looked at a sample problem where three forces acted on a beam and calculated the torque produced by each force. Forces applied directly on the axis of rotation do not contribute to torque and force that do contribute to torque could produce clockwise (-) or counterclockwise (+) rotation. When calculating τnet, pay close attention to those signs. On Monday, C Block will work on a lab that centers on torque and rotational equilibrium and F Block will move on to take a look at center of mass and moment of inertia.
Which was what B Block discussed today. An object's center of mass is the point on an extended object where it will naturally rotate around when acted on only by gravity. Toss a baseball bat in the air and it will rotate around its center of mass, but the center of mass itself will trace out the characteristic parabolic trajectory of an object demonstrating projectile motion. However, an object can rotate around any point if you apply a torque and some axes are easier to rotate around than others. That leads to the idea of moment of inertia - the resistance of an object to rotation. If the mass of an object is clustered around the rotational axis, the moment of inertia will be lower than if the mass is spread at a distance from the axis. We looked at a couple of demonstrations to see how mass distribution affects rotation, specifically angular acceleration, and we'll pursue that relationship mathematically in a later section. On Monday, we'll move into the arena of the second condition for equilibrium and see how to analyze objects in translational and rotational equilibrium.
E Block continued their lab work on rotational dynamics. All groups have their data now and will work on data analysis on Monday.
Have a good weekend!
B and F Blocks began their work with rotational dynamics with a study of torque. Remember that torque is not a force - it is the ability of a force to produce rotation. We looked at some examples of how lever arm affects what the force accomplishes when applied to a rotating body. And don't forget angle - only the component of the force that is perpendicular to the rotation contributes to torque and the formula:
takes those factors into account. We looked at a sample problem where three forces acted on a beam and calculated the torque produced by each force. Forces applied directly on the axis of rotation do not contribute to torque and force that do contribute to torque could produce clockwise (-) or counterclockwise (+) rotation. When calculating τnet, pay close attention to those signs. On Monday, C Block will work on a lab that centers on torque and rotational equilibrium and F Block will move on to take a look at center of mass and moment of inertia.
Which was what B Block discussed today. An object's center of mass is the point on an extended object where it will naturally rotate around when acted on only by gravity. Toss a baseball bat in the air and it will rotate around its center of mass, but the center of mass itself will trace out the characteristic parabolic trajectory of an object demonstrating projectile motion. However, an object can rotate around any point if you apply a torque and some axes are easier to rotate around than others. That leads to the idea of moment of inertia - the resistance of an object to rotation. If the mass of an object is clustered around the rotational axis, the moment of inertia will be lower than if the mass is spread at a distance from the axis. We looked at a couple of demonstrations to see how mass distribution affects rotation, specifically angular acceleration, and we'll pursue that relationship mathematically in a later section. On Monday, we'll move into the arena of the second condition for equilibrium and see how to analyze objects in translational and rotational equilibrium.
E Block continued their lab work on rotational dynamics. All groups have their data now and will work on data analysis on Monday.
Have a good weekend!
11/17/11
Rotational Dynamics
C and F Blocks had their graded learning experiences for circular motion today and will move into rotational dynamics tomorrow.
B Block sat down and took a good hard look at the concept of torque, the rotational analogue of force. Torque depends not only on the magnitude of the applied fore, but also the location of the force relative to the axis of rotation. The angle at which the force is applied also matters, as only the force component that is perpendicular to the rotational arm contributes to torque. We looked at a variety of examples that highlighted the role of lever arm and angle on torque and took time to nail down the mathematical finery of the topic. Tomorrow, we'll expand on the contrast between point masses and extended objects by taking on center of mass and rotational equilibrium.
E Block began work on their rotational dynamics lab. Took folks awhile to get comfortable working with the equipment, but all groups were actively collecting angular acceleration data by the period's end. Tomorrow, we will continue to examine the relationship between torque, angular acceleration and moment of inertia. Take time tonight to plan out tomorrow's data collection and, perhaps, doing some reading on moment of inertia.
11/16/11
Turning the Corner
C and F Blocks put the final nail in the circular motion coffin and will bury it tomorrow with their exam. Then, it's off into other aspects of rotational motion such as torque, moment of inertia, angular momentum...
B Block did some reading and thinking on the subject of torque - the ability of a force to produce rotation. The application of a force is not the final word in the rotation of an object. We have to take into account where the force is applied, which is spelled out in the concept of lever arm. A force applied at a distance from a rotational axis makes for easier rotation than a force applied close to the axis. Think about spinning a bike wheel by putting your hand on the rubber of the tire, or using your finger down near the axle to spin the tire using the spokes. One is easy and one is hard. We'll go into this in detail tomorrow and your lab for this unit will let you quantify this relationship, while dragging in the concept of moment of inertia, to boot. E Block had the day off, so nothing to say about them, but "see you tomorrow" and be ready to work on your rotational dynamics lab investigation.
B Block did some reading and thinking on the subject of torque - the ability of a force to produce rotation. The application of a force is not the final word in the rotation of an object. We have to take into account where the force is applied, which is spelled out in the concept of lever arm. A force applied at a distance from a rotational axis makes for easier rotation than a force applied close to the axis. Think about spinning a bike wheel by putting your hand on the rubber of the tire, or using your finger down near the axle to spin the tire using the spokes. One is easy and one is hard. We'll go into this in detail tomorrow and your lab for this unit will let you quantify this relationship, while dragging in the concept of moment of inertia, to boot. E Block had the day off, so nothing to say about them, but "see you tomorrow" and be ready to work on your rotational dynamics lab investigation.
11/15/11
Still Circiln'
B and E Blocks took their circular motion exam today and will move on to rotational dynamics tomorrow/Thursday. With the half-day in place, only B Block will meet, but E Block has their marching orders to prepare for Thursday's law on rotational motion.
C and F Blocks did some review work after going over their universal gravitation problems. Tomorrow, F Block will run their centripetal force lab and B will get a bit more review for Thursday's exam.
C and F Blocks did some review work after going over their universal gravitation problems. Tomorrow, F Block will run their centripetal force lab and B will get a bit more review for Thursday's exam.
11/14/11
Back in the Saddle
After a long weekend, we hop right back into circular motion for the final blast before we hit rotational dynamics. B and E Blocks went over their homework for gravitational/centripetal forces and reviewed for tomorrow's exam. No very complex problems, but a lot of little ones to make sure you can work with the skills in the chapter. Still only 25 test items, though, and the short answer should be guaranteed points if you haven't been sleeping in class.
C and F Blocks reviewed their work on centripetal force and took a look at Newton's Law of Universal Gravitation today. Gravity is generated by all mass and the larger the mass, the stronger the gravitational field. As with all fields, as you distance yourself from the mass, the field gets weaker. So, combine those ideas and we get the notion that the force that arises when two gravitational fields overlap is directly proportional to the masses and inversely proportional to the distance between them. Specifically:
Fg = G(m1m2)/r2
This is an example of an inverse-square law, and we'll see several of them this year. Tonight's homework will allow you to practice with this formula and remember the head's ups I gave you in class: don't forget "G," don't forget to square/square-root the distance and make sure you can work with your calculator efficiently to punch in all those darned numbers and exponents. Although none of the problems have you work with a distance between two objects and then add the individual radii for your overall calculation, don't lose sight of the fact that the distance is measured between each object's center of gravity which, for a sphere is dead smack in the middle. We'll go over these problems tomorrow and start the review process for Thursday's exam.
C and F Blocks reviewed their work on centripetal force and took a look at Newton's Law of Universal Gravitation today. Gravity is generated by all mass and the larger the mass, the stronger the gravitational field. As with all fields, as you distance yourself from the mass, the field gets weaker. So, combine those ideas and we get the notion that the force that arises when two gravitational fields overlap is directly proportional to the masses and inversely proportional to the distance between them. Specifically:
This is an example of an inverse-square law, and we'll see several of them this year. Tonight's homework will allow you to practice with this formula and remember the head's ups I gave you in class: don't forget "G," don't forget to square/square-root the distance and make sure you can work with your calculator efficiently to punch in all those darned numbers and exponents. Although none of the problems have you work with a distance between two objects and then add the individual radii for your overall calculation, don't lose sight of the fact that the distance is measured between each object's center of gravity which, for a sphere is dead smack in the middle. We'll go over these problems tomorrow and start the review process for Thursday's exam.
11/9/11
Nice Short Week
We'll pick up education again on Monday, so enjoy your long weekend...
B Block conducted their centripetal force lab, investigating centripetal force, tangential velocity and rotational radius. From our discussion of centripetal force and acceleration, the results should not have been surprising. For a given force, a larger radius requires a larger velocity and as force increases, greater velocity is required to maintain constant radius. On Monday, we'll go over the lab, the homework problems on centripetal force and gravity and review for Tuesday's exam.
C Block worked through tangential velocity and acceleration, with centripetal acceleration and force thrown in for fun. Remember to use the correct units for angular variables and linear variables and that tangential acceleration has a different job than centripetal acceleration. Tangential acceleration reports rate of change of direction, centripetal acceleration reports rate of change of speed. That tangential velocity vector has two components and each acceleration measures rate of change in one of them. It stands to reason, then, that centripetal force produces change of direction of velocity, and you would be right. We'll review these ideas on Monday before starting to work on gravity.
E Block did their own force work today with centripetal force and gravity. Remember that many forces can act as centripetal forces, including gravity, but do not always serve that function in all situations. Work on those homework problems and pay special attention to the gravity piece - that formula gets people into trouble if they forget about the /r2 piece.
F Block reviewed tangential velocity/acceleration and centripetal acceleration before moving in to centripetal force. We took time to discuss the basic job of centripetal force and looked at examples of how various forces can take on that role. On Monday, we'll take a special look at gravity - a force produced by all matter.
B Block conducted their centripetal force lab, investigating centripetal force, tangential velocity and rotational radius. From our discussion of centripetal force and acceleration, the results should not have been surprising. For a given force, a larger radius requires a larger velocity and as force increases, greater velocity is required to maintain constant radius. On Monday, we'll go over the lab, the homework problems on centripetal force and gravity and review for Tuesday's exam.
C Block worked through tangential velocity and acceleration, with centripetal acceleration and force thrown in for fun. Remember to use the correct units for angular variables and linear variables and that tangential acceleration has a different job than centripetal acceleration. Tangential acceleration reports rate of change of direction, centripetal acceleration reports rate of change of speed. That tangential velocity vector has two components and each acceleration measures rate of change in one of them. It stands to reason, then, that centripetal force produces change of direction of velocity, and you would be right. We'll review these ideas on Monday before starting to work on gravity.
E Block did their own force work today with centripetal force and gravity. Remember that many forces can act as centripetal forces, including gravity, but do not always serve that function in all situations. Work on those homework problems and pay special attention to the gravity piece - that formula gets people into trouble if they forget about the /r2 piece.
F Block reviewed tangential velocity/acceleration and centripetal acceleration before moving in to centripetal force. We took time to discuss the basic job of centripetal force and looked at examples of how various forces can take on that role. On Monday, we'll take a special look at gravity - a force produced by all matter.
11/8/11
Tossing in Tangentials
E and F Blocks added tangential velocity and acceleration to our descriptors of circular motion. Both are instantaneous values with a straight line direction found through drawing the tangent line for the relevant point on the circle. Unlike angular velocity and acceleration, these values are not the same for every point on the object - they vary based on distance from the axis of rotation. The further away from the rotational axis, the larger they are and they decrease in size as we approach the center of the circle. Centripetal acceleration describes the rate of change of direction for the tangential velocity vectors and always points to the center of the circle. Make sure you can use both formulas to calculate centripetal acceleration, based on the velocity value you're given and we'll add in the force that promotes this acceleration tomorrow.
B Block discussed centripetal force in class and related it to our work yesterday on centripetal acceleration. Remember that "centripetal force" is a job description - many forces can serve this purpose and you might have to calculate the value of the centripetal force using Newton's nd Law of Motion or assess a normal force before moving on in a problem. We also began our discussion of gravity, which was cut short by the fire drill. Gravity is a force of attraction between all matter and can be calculated using Newton's Law of Universal Gravitation. We'll review this tomorrow very briefly before you start on your lab investigation.
C Block worked on their centripetal force lab, looking at the relationship between centripetal force, radius of rotation and speed of rotation. For your write-up, you only have to include the graphs, data tables and a concluding statement about the relationship between force and velocity versus force and velocity2. We'll go over these tomorrow and use the lab to highlight some ideas about centripetal acceleration.
B Block discussed centripetal force in class and related it to our work yesterday on centripetal acceleration. Remember that "centripetal force" is a job description - many forces can serve this purpose and you might have to calculate the value of the centripetal force using Newton's nd Law of Motion or assess a normal force before moving on in a problem. We also began our discussion of gravity, which was cut short by the fire drill. Gravity is a force of attraction between all matter and can be calculated using Newton's Law of Universal Gravitation. We'll review this tomorrow very briefly before you start on your lab investigation.
C Block worked on their centripetal force lab, looking at the relationship between centripetal force, radius of rotation and speed of rotation. For your write-up, you only have to include the graphs, data tables and a concluding statement about the relationship between force and velocity versus force and velocity2. We'll go over these tomorrow and use the lab to highlight some ideas about centripetal acceleration.
11/7/11
Round and Round We Go
Everyone was swimming in the rotational motion pool today and we'll keep on with circular motion concepts for one more chapter when this one is done...
C and F Blocks got their introduction to circular motion with a basic description of what circular motion entails and how to measure and describe the motion. Displacement is viewed from the standpoint of how much of the circle covered and is reported as an angle. Remember to have your calculator in radians for this unit, since this is how we will work with angles in this unit. Once displacement has been defined as an angle, the calculation of angular velocity and acceleration follows in the same fashion as for linear motion: ω = ΔΘ/time and α = Δω/time. For kinematics formulas, use the ones you're used to and substitute the angular version of the variable for its linear counterpart. Pay attention in problem solving for how displacement is reported, as there a few ways that it can be presented - 15 radians, 3πradians, 6 revolutions, 4 laps around the track - and you have to make the appropriate conversions for your problem solving. We'll go over the homework problems first thing tomorrow in F Block, then move into tangential (or linear) velocity and acceleration and take a peek at a third acceleration: centripetal acceleration. C Block will be conducting a lab investigation on centripetal acceleration and force that will give folks a look ahead to those topics.
B Block worked through tangential velocity and acceleration, as well as centripetal acceleration. Tangential velocity and acceleration are instantaneous values and exist for every point on the circle. Every part of the rotating object has a set of motion conditions that if there was no centripetal force, would dictate the motion of the object. If you whirl a ball on a string and snip the string, the ball would move in a straight line and speed as indicated by the tangential motion values. Unlike angular velocity and acceleration, tangential values are not the same for every point on the circle - the farther away from the axis of rotation you are, the greater are these values. In fact, it is the differences in the tangential variables that produce constant angular values. Centripetal acceleration is responsible for fiddling with the direction portion of the tangential velocities and is always directed perpendicular to the tangential acceleration and directed towards the center of the rotation. You'll get to play with this acceleration on Wednesday in your lab investigation, but make sure you can calculate it now, either with rotational or tangential velocity as the given velocity value.
E Block began their discussion of rotational motion after an overview of Friday's lab investigation. Objects moving in a circle have the same descriptors of motion as linear motion - displacement, velocity, acceleration, etc. and after a re-imagining of how displacement is reported, the calculation and analysis of angular velocity and acceleration follows easily. Tonight, you are working on angular kinematics - remember to read the problems carefully, use units to identify variables, pay close attention as to who is initial and who is final velocity and be mindful of signs. We'll go over this work tomorrow before adding another type of velocity and two types of acceleration to our descriptors list.
C and F Blocks got their introduction to circular motion with a basic description of what circular motion entails and how to measure and describe the motion. Displacement is viewed from the standpoint of how much of the circle covered and is reported as an angle. Remember to have your calculator in radians for this unit, since this is how we will work with angles in this unit. Once displacement has been defined as an angle, the calculation of angular velocity and acceleration follows in the same fashion as for linear motion: ω = ΔΘ/time and α = Δω/time. For kinematics formulas, use the ones you're used to and substitute the angular version of the variable for its linear counterpart. Pay attention in problem solving for how displacement is reported, as there a few ways that it can be presented - 15 radians, 3πradians, 6 revolutions, 4 laps around the track - and you have to make the appropriate conversions for your problem solving. We'll go over the homework problems first thing tomorrow in F Block, then move into tangential (or linear) velocity and acceleration and take a peek at a third acceleration: centripetal acceleration. C Block will be conducting a lab investigation on centripetal acceleration and force that will give folks a look ahead to those topics.
B Block worked through tangential velocity and acceleration, as well as centripetal acceleration. Tangential velocity and acceleration are instantaneous values and exist for every point on the circle. Every part of the rotating object has a set of motion conditions that if there was no centripetal force, would dictate the motion of the object. If you whirl a ball on a string and snip the string, the ball would move in a straight line and speed as indicated by the tangential motion values. Unlike angular velocity and acceleration, tangential values are not the same for every point on the circle - the farther away from the axis of rotation you are, the greater are these values. In fact, it is the differences in the tangential variables that produce constant angular values. Centripetal acceleration is responsible for fiddling with the direction portion of the tangential velocities and is always directed perpendicular to the tangential acceleration and directed towards the center of the rotation. You'll get to play with this acceleration on Wednesday in your lab investigation, but make sure you can calculate it now, either with rotational or tangential velocity as the given velocity value.
E Block began their discussion of rotational motion after an overview of Friday's lab investigation. Objects moving in a circle have the same descriptors of motion as linear motion - displacement, velocity, acceleration, etc. and after a re-imagining of how displacement is reported, the calculation and analysis of angular velocity and acceleration follows easily. Tonight, you are working on angular kinematics - remember to read the problems carefully, use units to identify variables, pay close attention as to who is initial and who is final velocity and be mindful of signs. We'll go over this work tomorrow before adding another type of velocity and two types of acceleration to our descriptors list.
11/5/11
11/4/11
That Time of Year
The Child's Play initiative has officially kicked off for the year! A charity built by the twisted minds behind the Penny Arcade webcomics to support sick children, it gives gamers a chance to show the world that we're not the stereotypical social rejects or violence-crazed nutcases as the media likes to paint us. Donations can be made through PayPal or texting, or you can choose a hospital (I support Children's Hospital in Boston) and click through to their Amazon WishList to buy things to send directly to kids in need. There are a variety of other ways to participate, like donating to Desert Bus for Hope or even creating your own fundraising event like a gaming marathon, so interested folks can find some way to toss their hat into the ring. Times are tough, so it is not easy sometimes to part with any dollars, but if you can do anything, some very sick child would be more grateful than you can imagine. Visit the Child's Play site for more information and try to give a hospital-bound kid a smile...
Many Happenings
B Block worked through angular kinematics today, building on last night's reading. After we frame displacement in terms of angles (measured in radians!), calculating angular velocity and acceleration follow the same techniques that we used for linear motion. For the kinematics formulas, they are item-for-item substitutions between the linear variables and their angular counterparts. Same formulas, different motion. We'll review this ground on Monday before tacking on tangential speed and tangential acceleration.
C and F Blocks worked on their test corrections in class due to the time constraints for getting grades submitted. Have them ready for Monday and that will be our official start day for rotational motion.
E Block worked on their centripetal force investigation, looking at the relationship between the magnitude of the force, the rotational radius and the rotational speed. The greater the force, the faster the speed had to be to maintain a constant radius and a smaller radius required less speed to be maintained than a large radius, when the forces were equal. We'll get into deeper discussion of centripetal force and acceleration on Tuesday - Monday is set aside to explore the basics of angular kinematics.
Have a good weekend!
C and F Blocks worked on their test corrections in class due to the time constraints for getting grades submitted. Have them ready for Monday and that will be our official start day for rotational motion.
E Block worked on their centripetal force investigation, looking at the relationship between the magnitude of the force, the rotational radius and the rotational speed. The greater the force, the faster the speed had to be to maintain a constant radius and a smaller radius required less speed to be maintained than a large radius, when the forces were equal. We'll get into deeper discussion of centripetal force and acceleration on Tuesday - Monday is set aside to explore the basics of angular kinematics.
Have a good weekend!
11/3/11
A Lost Day
I was closeted with a number of my brethren getting training on a piece of software for curriculum mapping (yes, it was as big-sighing as it sounds)so you guys had the run of the day. Well, not quite...
B and E Blocks dipped their toes into rotational motion with basic descriptors of rotational motion such as angular displacement, velocity and acceleration. Once you re-define how we measure displacement for circular motion, the rest just falls into place. B Block will discuss this material tomorrow and E Block will conduct a lab activity on centripetal acceleration and force. Something has to work on changing the direction of the object so that it moves in a circle...
C and F Blocks watched the Mythbusters episode, Ping Pong Rescue, that introduced concepts about buoyancy and forces in fluids. Is this our next chapter? No. But it did let you see how basic observations and experiments work to produce the concepts that we discuss and formulas that we use. Make sure to finish up your discussion questions to go over tomorrow - we will get to forces in fluids in a couple of chapters so your brainwork is not wasted. Tomorrow, owing to the large number of individuals who need to make up the Chapter 6 exam and the looming deadline for submitting Quarter 1 grades, time will be allotted for test corrections and test taking so we can end the quarter with everyone up to date.
See you tomorrow!
B and E Blocks dipped their toes into rotational motion with basic descriptors of rotational motion such as angular displacement, velocity and acceleration. Once you re-define how we measure displacement for circular motion, the rest just falls into place. B Block will discuss this material tomorrow and E Block will conduct a lab activity on centripetal acceleration and force. Something has to work on changing the direction of the object so that it moves in a circle...
C and F Blocks watched the Mythbusters episode, Ping Pong Rescue, that introduced concepts about buoyancy and forces in fluids. Is this our next chapter? No. But it did let you see how basic observations and experiments work to produce the concepts that we discuss and formulas that we use. Make sure to finish up your discussion questions to go over tomorrow - we will get to forces in fluids in a couple of chapters so your brainwork is not wasted. Tomorrow, owing to the large number of individuals who need to make up the Chapter 6 exam and the looming deadline for submitting Quarter 1 grades, time will be allotted for test corrections and test taking so we can end the quarter with everyone up to date.
See you tomorrow!
11/2/11
Test Day!
Everyone was engaged with their exams today and tomorrow would have been the official start of circular motion, but I have to spend the day with some curriculum mapping software. Oh, the fun... I can already feel the fun...
Anyway, you'll be busy tomorrow, so don't think it will be a day off. We'll pick up with angular displacement, speed and acceleration on Friday, with E Block working on a lab involving centripetal acceleration and force.
Anyway, you'll be busy tomorrow, so don't think it will be a day off. We'll pick up with angular displacement, speed and acceleration on Friday, with E Block working on a lab involving centripetal acceleration and force.
11/1/11
Contact Lenses
Everyone asks me where I get my contact lenses for my Halloween costume and it is this company:
9mm Special Effects
They provide special effects contact lenses for film, TV and videos - in other words, they know what they're doing to get a good effect that is safe for the wearer. If you ever want to add contact lenses to your Halloween costume, and a number of you say this every year, you HAVE TO shop with a reputable company. Cheap contact lenses can ruin your eyes - you need quality lenses and a good company will accommodate any prescription you might have. Yes, professionally-crafted lenses will cost a bit, but your eyes are worth it...
9mm Special Effects
They provide special effects contact lenses for film, TV and videos - in other words, they know what they're doing to get a good effect that is safe for the wearer. If you ever want to add contact lenses to your Halloween costume, and a number of you say this every year, you HAVE TO shop with a reputable company. Cheap contact lenses can ruin your eyes - you need quality lenses and a good company will accommodate any prescription you might have. Yes, professionally-crafted lenses will cost a bit, but your eyes are worth it...
NPR's 100
National Public Radio asked listeners to help with a list of the top 100 SciFi/Fantasy books. SF Signal made up a great flow-chart to help you choose something from the list to read. The .jpg is a big image that takes little scrolling to navigate but is a very cool image to work with. If you'd like an interactive version - check out this link: An Interactive Guide to NPR's List of Top 100 Science Fiction and Fantasy books.
Countdown to Test Time
Today was a day of review for all sections. The review sheet has been up online and folks have hopefully availed themselves of that resource. In class, we walked through the chapter, page by page highlighting relevant material and skills and took time to answer any questions people threw out. On Thursday, I'll be out due to some training they want people to have for some software the district is buying, so our formal start to circular motion work will begin on Friday. Good luck tomorrow!
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