# Rolling cylinder on cylindrical plane

See attached

## Homework Equations

K.E (rotational) = .5*I*omega^2
K.E (translational) = .5*m*v^2

## The Attempt at a Solution

v(of rod and translational vel of cylinder) = L * (dαlpha/dt)

Is the angular velocity of the cylinder the same as the angular velocity of the rod?
To calculate the translational K.E of the cylinder can I use the vel i've calculated above for the rod?
For the rotational vel of the cylinder, can i use I (com) = 0.5*m*r^2

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Is the angular velocity of the cylinder the same as the angular velocity of the rod?
The angular velocity of the CM of the cylinder about O will be equal to the angular velocity of the rod about O. But the cylinder has a different angular velocity wrt its CM.

To calculate the translational K.E of the cylinder can I use the vel i've calculated above for the rod?
Yes.

For the rotational vel of the cylinder, can i use I (com) = 0.5*m*r^2
Yes. But to find the MI about O, you have use parallel axis theorem.