Yes, you're right! D is the distance from the centre of mass axis (axis of symmetry).
Always remember: The moment of inertia Icm is always with respect to the centre of mass, from which there is a symmetric distribution of mass (at least for homogeneous rigid bodies). So whenever you need to...
Everything looks correct.
You're right, from the torques acting on the pulley you get:
T2-T1=[(Mass of the pulley)*R*α]/2 = (I*α)/R
and from the no slip condition you know that α=a/R therefore
T2-T1=[(Mass of the pulley)*a]/2 = (I*a) / R^2
and solving for a, you get...
What I thought was that because the plank can slide over the horizontal smooth surface and assuming Force < Max static friction, then the cylinder will start rotating but the centre of mass will not undergo translational motion and then the velocity will be = 0 (all with respect to a reference...
Yes, you're right Mister. Although the problem says nothing about friction between the plank and the cylinder, I thought because of the condition of pure rotation there must be static friction, otherwise the cylinder would just slip.
https://lh3.googleusercontent.com/-FQFbA0n6chNSwQwUE9jUwaEgA_EDDnwEXjPbTQBRg=w1366-h768-rw
Here is the diagram. If you can't see it here is the set-up
The cylinder is on top of the plank, and the plank lies in a smooth horizontal frictionless surface. The cylinder has a radius R and also a...