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.