It is well known that for a hollow, cylindrical shell rolling without slipping on a horizontal surface, half of the total kinetic energy is translational and half is rotational. what fraction of the total kinetic energy is rotational for the following objects rolling without slipping on a horizontal surface? part aa uniform solid cylinder. part ba uniform sphere. part ca thin-walled hollow sphere. part da hollow, cylinder with outer radius r and inner radius r/2.

Part a)

B) uniform Sphere

C) uniform hollow sphere

D) uniform hollow cylinder with inner radius R/2 and outer radius R

Explanation:

As we know that fraction of total energy as rotational energy is given as

now we have

now we have

A) uniform Solid cylinder

for cylinder we know that

B) uniform Sphere

for sphere we know that

C) uniform hollow sphere

for hollow sphere we know that

D) uniform hollow cylinder with inner radius R/2 and outer radius R

for annular cylinder we know that

if you already have the answer to (a), then just work out how many periods there are in 1 minute, and that's the answer to (c).