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 v_t and ω can be interchanged using the relationship we learned last chapter:

v_t = 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 (KE_rot = 1/2 I(v_t²/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.