Rotational and Kinetic Energy - Down a Hill

[PeachBanana]

Homework Statement

15. Three objects with the same total mass and radius, a hoop, a disk, and a sphere each
roll without slipping down an incline. Which of the following statements is FALSE?

A) The hoop has the largest moment of inertia, so it arrives at the bottom first.
B) The object with the largest rotational kinetic energy has the smallest translational
kinetic energy.
C) Each of the objects has the same total kinetic energy at the bottom of the incline.
D) Total energy is conserved in each case.

Homework Equations

Hoop: I = Mr^2
Sphrere: I = (2/5)Mr^2
Disk: I = (1/2)Mr^2

The Attempt at a Solution

K.E. tot = Rotational + kinetic
K.E. tot (hoop for example) = 1/2 Iω^2 + 1/2 mv^2

Hmm. Energy is always conserved, so I want to say that makes "C" true too. I'm unsure about "A" and "B."

 

[jbsteele]

A seems true to me, since the hoop has the largest moment of inertia, so it should take the longest time to accelerate, so it would arrive at the bottom first. B is false, since the object with the largest rotational kinetic energy will have the largest total kinetic energy. Answer: B) The object with the largest rotational kinetic energy has the smallest translational kinetic energy.