A solid ball (I_S = 2/5 MR²) and a hollow ball (I_H = 2/3 MR²) are both rolling without slipping along a paved, level path, both at a constant speed for now. Both balls have the same rotational inertia: I_S= I_H. Since you'll be moving back and forth between the two balls, despite one being assigned to you for #1, always S and H subscripts for all qtys that are different for the two balls, and identify them as solid or hollow (not "my ball" and "other ball"). (1) MVQ, RNG If you were born in an even month (Feb, April, June, etc.) then the two balls have the same mass M. Otherwise (odd month), the two balls have the same radius R. If your first name has an even number of letters, you're assigned the solid ball; otherwise the hollow ball. Choose M = 3.74 kg and R = 18.2 cm for your assigned ball. Either M or R is the same for both balls. State the two parts of the question version assigned to you, identify your randoms, then calculate the unknown quantity (either R or M), for the other ball, using the fact that the balls have the same rotational inertia. Check: are I_S and I_H equal? Use S and H subscripts for all qtys not equal for both balls.. (2) MVQ, RNG If the 3rd-to-last digit of your phone is odd, both balls are rolling at the same translational speed v; otherwise, they're rolling at the same angular speed . If the balls have the same translational speed, choose V = V_S = V_H =7.13 m/s for both balls, leaving _S and _H initially unknown. But if they have the same angular speed, choose = _S = _H = 29.5 rad/s for both balls, leaving v_S and v_H initially unknown. State your question version along with your random, then calculate the two unknown speeds, either v_S and v_H or _S and _H. (3) Calculate the total kinetic energy of the ball assigned to you in #1. Use S or H subscripts to make clear which ball you're working on. (4) The path the balls are rolling along runs up a hill tall enough that they'll eventually stop rolling for an instant, before rolling back downhill again, though they don't roll to the same height. Calculate the maximum height that your assigned ball reaches when rolling uphill, assuming its total mechanical energy is conserved. Start from Ei = Ef , show all steps, and maintain i/f (initial/final) subscripts until numerical values are substituted. (5) Calculate the translational speed v of the other ball (not the ball in #4), when it has rolled to a height exactly half of the height your asssigned ball stops at in #4. For example, if you were assigned the hollow ball in #1, and in #4 found that it stopped at a height of 8.00 m, then in this question, you'd calculate the speed vS of the solid ball when the solid ball has reached a height of 4.00 m.

This one is more challenging than #4, since the ball isn't at rest at the beginning or end. Remember that the ball has two kinds of kinetic energy, and neither one is zero or contstant, so none of the kinetic energy terms will cancel out in any way. Starting from Ei = Ef is again required. If you hold off on subsituting numerical values, patience with the algebra is rewarded by some very helpful simplifications.