Question

A cylinder rolls up an inclined plane, reaches some height and then rolls down (without slipping through these motions). The direction of the frictional force acting on cylinder is/are:

Answer 1

We can easily find the direction of frictional force acting on the cylinder if we have a good understanding of friction and the direction in which it acts. So, in order to find the answer to the given question, first of all we need to find out the direction of force and then we need to relate the frictional force in its opposite direction.

Complete answer:
As we know that, there is always a force which is equal and opposite in nature acting in the opposite direction of motion. This force is only known as force of friction. Also, we know that frictional force opposes the relative motion between two surfaces.
Now, when the cylinder rolls up, due to the rotational motion of the cylinder, the cylinder tries to roll and as a result the frictional force tries to oppose its motion and acts in the upward direction.
Similarly, when the cylinder rolls down, the vertical component of the force due to the mass of the cylinder tries to pull the cylinder in the downward direction as at a height there is no initial inertia in the cylinder. In doing so, the cylinder attains a translational motion and the frictional force acting in upward direction tries to oppose this translational motion.
From steps two and three we can conclude that the direction of frictional force will be in upward direction in both the cases when the cylinder is trying to roll down and roll up on an inclined plane.

Note: Translatory motion can be defined as a type of motion in which all parts of the body cover the same distance with respect to time. On the other hand, linear motion is a type of motion, in which the body moves in a straight line. When in a body every particle of the body moves in a circle about a single line, then the motion is said to be rotational motion.