Question

A hoop rolls with constant velocity and without sliding along level ground. Its rotational kinetic energy is:______a- half its translational kinetic energyb- the same as its translational kinetic energyc- twice its translational kinetic energyd- four times its translational kinetic energy

Answer 1

The same as its translational KE.

The easy way to do this is to make up numbers and use them.

So, I'll say m=2 and r=3. I will also say v=3 .

Rot. Inertia of a hoop is mr^2. So the rot KE is: 1/2 (mr^2)(w^2)

note: (1/2*I*w^2)

Translational kinetic energy is basically normal KE, so 1/2(m)(v^2)

Now, lets plug our made up values in:

Rot Ke : 1/2 (9*2)(3/3) *note w = v/r

Tran Ke: 1/2(2)(9)

Rot Ke: 9

Tran Ke: 9

9=9, same.