Solving for Acceleration and Friction in Rolling Motion

[iitjee10]

Here's the question:

A solid sphere of mass M is being pushed by a plank of mass m along the top of the rim.
Assuming pure rolling at all points of contact, find:
(i) the accelerations of the centre of mass sphere and the plank w.r.t. ground.
(ii) frictional forces operating at both the contacts.

 

[rcgldr]

It might help to think of this similar to a pulley problem. The surface on the bottom is the equivalent of a fixed string, the surface on the top is equivalent to a string being accelerated. In this case, there's no gravity, just inertia of the sphere keeping the string taught.

 

[Doc Al]

Here's the question:

A solid sphere of mass M is being pushed by a plank of mass m along the top of the rim.
Assuming pure rolling at all points of contact, find:
(i) the accelerations of the centre of mass sphere and the plank w.r.t. ground.
(ii) frictional forces operating at both the contacts.

Attack this in the usual manner. Analyze the forces acting on plank and sphere and apply Newton's 2nd law to each. You'll end up with three equations (two for translational motion; one for rotation).

Hint: How is the acceleration of the plank related to the acceleration of the sphere?