I am facing trouble with the following problem.
A solid cylinder of mass M=5kg rests on two supports of same height as shown.One support is rough and stationary while other is am smooth plank of same mass M=5kg placed on a smooth horizontal surface.Initially $\theta=37 degree and there is no slipping between the cylinder and stationary support.The support is released from rest.
The question is to find out the acceleration of cylinder just after release.
I drew a free body diagram of the body.
Since friction force is the only tangential force acting on the sphere .So $fR=(1/2)mR^2( a/R)$ where $a$ is the acceleration of the cylinder.This gives $f=ma/2$.Also since one of the block is stationary.The component of forces along that direction should reduce to zero.So resolving forces in the perpendicular direction we get $$mgcos(\theta)-N_1sin(2\theta)-f=ma$$.All things are known except for $ N_1$.I am facing trouble in finding out $N_1$ in terms of the acceleration of the cylinder.Any hint to go ahead will be highly appreciated.Thanks.