Practicing with Moment of Inertia, Newton's Second Law for rotation, Rotational Kinetic Energy, and Angular Momentum Q1: Rank in order, from largest to smallest, the angular accelerations da to de of the rigid objects in cases (a)-(e) shown in the figure below. Explain your ranking (a) (b) (c) 2 NA IN 4 kg INA 2 kg 2 kg 2 m 2 m 2 m 2 kg 2 kg VIN 4 kg V2 N (d) (e) 2 N IN 2 kg 2 kg 4 m 4 m - 130 30' L 2 kg 2 kg N 2 N Q2: A solid cylinder, a solid sphere, and a hoop, all three of mass M and radius R, are given in the figure below: Imagine all three of these shapes (the solid sphere, the cylinder, and the hoop), all start with their Centers of Mass a height h above the ground, at the top of an incline of horizontal angle 0. This 'common starting point' corresponds to each shape being a distance L along the incline. See figure below: O h Given the above setup, assume that all three shapes are released from rest at the same time, and that each shape rolls down the incline without slipping. Which one will 'win the race' to the bottom of the incline? That is, which shape will reach the bottom of the incline in the least amount of time? Answer this question. Justify your answer mathematicallyQ3: A diver, with arms outstretched. [deliberately and safely] falls from rest, straight down from a diving board high enough off the ground for the diver to 'have time to do everything described below'. The height of the diving board is still low enough to the ground that you can ignore the effects of air drag on the diver. "he diver starts with arms outstretched and Center of Mass in freefall {described above): {1] "he diver brings their arms in close to their body during the freefall, and this puts them into a spin about an axis of rotation through their Center of Mass. The Center of Mass of the Diver is still in freefall, but the diver is now also spinning {a bout their Center of Mass with angular speed U12: {2} After 'spinning in freefall' like this for a while, the diver then stretches their arms out 'a little bit', such that their arms are no longer as close to their body, but such that their arms are nowhere near to being 'outstretched all the way' as they were in [1]. The diver, with arms slightly farther away from their body than in [2] is still 'spinning in freefall': (3} The question is, now that the diver is in BI: are they sginning with an angular speed, wgthat is greater thanI egual toI or less than their angular speed in [21, mg. In other words, is Luann. is waqoz. or is w3=u12? Justify your answer. - Getting Started: State the important information and summarize the problem. If possible, include a diagram. Note any assumptions you're making. - Devise Plan: Devise a plan of attack before diving into the solution. Break down the problem into smaller, manageable segments. Identify which physical relationships you can apply. - Execute Plan: Carry out your plan, explaining each step. The argument should be easy to follow. Articulate your thought process at each step {including roadblocks]. Any variables should be clearly defined. and your diagrams should be labeled. - Evaluate Solution: Check each solution for reasonableness. There are many ways to justify your reasoning: check the symmetry of the solution, evaluate limiting or special cases, relate the solution to situations with known solutions, check units, use dimensional analysis, andfor check the