PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
Two space-station exercise wheels, C and D, have the same mass M and outer radius R.
• Wheel C is a solid disk spinning with angular speed ωC.
• Wheel D is a thin ring spinning with angular speed ωD.
Assume both wheels rotate about their central axes in a region free of external torques.
(a) Rank the wheels by rotational kinetic energy when ωC=ωD. Justify your answer without numeric calculation.
(b) Derive an algebraic expression for the angular speed ωD that will make the rotational kinetic energies of the two wheels equal.
(c) If the solid disk spins at ωC=30rads−1, calculate the angular speed required for the thin ring to match its rotational kinetic energy.
(d) Explain, in terms of how mass is distributed relative to the axis, why the thin ring must spin faster than (or slower than) the disk to achieve the same rotational kinetic energy.