Question

Consider a cylinder of mass M resting on a rough
horizontal rough that it pulled out from under it with
acceleration 'a' perpendicular to the axis of cylinder. What
is Ffriction at point P? It is assumed that the cylinder does
not slip??
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Answer 1

Explanation:

Given Consider a cylinder of mass M resting on a rough  horizontal rough that it pulled out from under it with  acceleration 'a' perpendicular to the axis of cylinder. What  is friction at point P?

Consider a cylinder of mass M resting on a rough surface.  We know the  types rolling motion that is pure rolling, slipping motion skidding motion.

Cylinder does not slip and rests on a rough  horizontal rough surface.

Due to translation α = F/m

Angular acceleration of point p

So α = T/I

       = F x r / I

      = F x r / mr^2 / 2

     = 2 F / m r

Now acceleration of P due to translation and rotation will be

F / m + 2 F / mr x r

So α = 3 F / m

Or F = ma / 3