Question

The type of constraints on the mechanical system consisting of a cyllinder rolling (and possibilly sliding) down an inclined plane of angle alpha are? (please try to explain the reasons also)

Answer 1

As per the given question,

When a cylinder is rolling on the inclined plane, then the frictional force is acting on the block in the upward direction.

$mg\sin\theta$ is working downwards, which will try to rotate this cylinder due to which it's speed will start to increase that is called the rotational acceleration.

$I\alpha= mg \sin \theta R$

$\Rightarrow \alpha =\frac{R mg \sin \theta }{I}$

if the block which is on the inclined plane is not a cylindrical, then the frictional force is working which is greater than the frictional force on the cylinder. and the downward acceleration of the block will be $mg \sin \theta-f_s$ that will lead decrease the acceleration of the block with respect to rotational acceleration.