Answer to Question #138921 in Classical Mechanics for dwight

Question

A uniform solid cylinder, a hollow cylinder, and a uniform solid sphere are rolling at the same speed on a horizontal table without slipping. If they all have the same mass and radius, which statement is true?
A. They all have the same angular momentum.
B. The hollow cylinder has the most angular momentum.
C. The solid sphere has the most total kinetic energy.
D. The solid cylinder has the greatest rate of rotation.
E. They all have the same kinetic energy of rotation

Answer 1

$E_k=\frac{mV^2}{2} +\frac{\omega^2*I}{2}$

where $\omega$ rate of rotation $I$ moment of inertia

$m$ mass and $V$

$E_k$ kinetik energy

For rolling without slipping, ω = V/r

by the statement of the problem, all bodies have the same radius and speed, which means that the rate of rotation are equal

Angular moment $L =I*\omega$

for solid cylinder $I=\frac{1}{2}mr^2$

for hollow cylinder $I=mr^2$

for solid sphere $I=\frac{2}{5}mr^2$

Consequently the hollow cylinder has the most angular momentum.

ANswer: B. The hollow cylinder has the most angular momentum. is true