# Moments of inertia

Hi I have a few problems from 'Physics for Scientists and Engineers' by Serwat and Jewett, chap 10

Prob. 51

A cylinder of mass 10 kg rolls without slipping on a horizontal surface. At the instant its centre of mass has a speed of 10 m/s. Determine (a) the translational kinetic energy of its centre of mass (b) the rotational kinetic energy about its centre of mass (c) its total energy.

(a) turns out to be 500 J and (c) is the sum of E.K. rotational and E.K. translational however (b) is a mystery for me, I would appreciate someone helping me out.

Thanks.

Doc Al
Mentor
Hint: What does "rolling without slipping" mean?

Is that a hint or a question? If it's a hint I dont get the connection ... if it's a ques well in the rolling without slipping scenario velocity of the contact point (with the surface) is zero ... I know that if v of centre of mass will be half of the v at the top point. However for rotational kinetic energy I would need the moment of inertia, how do i calculate that? Btw the answer is 250 J, in case tht helps

Doc Al
Mentor
Is that a hint or a question?
Sure it's a hint! If it's a hint I dont get the connection ... if it's a ques well in the rolling without slipping scenario velocity of the contact point (with the surface) is zero ... I know that if v of centre of mass will be half of the v at the top point.
The condition for "rolling without slipping" gives you the relationship between translational and rotational speeds.
However for rotational kinetic energy I would need the moment of inertia, how do i calculate that?
What's the moment of inertia of a cylinder? Thanks Doc Al! :)