(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I think the problem was taken out from Landau&Lifgarbagez's book on classical mechanics.

An inhomogeneous cylinder of radius R rolls over a plane. The mass is distributed in such a way that a principal axis is parallel to the rotational axis of the cylinder and the center of mass is at a distance "a" from the rotational axis. The moment of inertia of the cylinder about the rotational axis is I. Calculate the kinetic energy of the cylinder.

2. Relevant equations

[itex]T=\frac{m v_{CM} ^2}{2}+ \frac{I \omega _c ^2 }{2}[/itex].

3. The attempt at a solution

The center of mass suffer from a circular motion of radius a and angular velocity [itex]\omega _c[/itex].

So that [itex]v_{CM}=a \omega _c[/itex] and thus [itex]T=\frac{\omega ^2 _c }{2} (ma^2 + I)[/itex].

This seems wrong to me because when a tends to 0, my kinetic energy equality tells me that there's only a rotational motion and no translational motion from the center of mass, which I believe it totally wrong.

I don't see what I did wrong though... I'd love some help to figure out what's wrong with what I did. Thanks in advance.

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# Kinetic energy of a rigid body

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