Question

A cylinder rolls up a hill, turns around, and starts rolling back down the hill. State the signs (+/-/0) of the angular acceleration and angular velocity at 3 points - one on the way up, one at the peak, and one on the way down. Briefly state your reasoning.

Answer 1

The cylinder would be at some angle with the horizontal straight line. Let the angle that line if motion of cylinder makes with the horizontal be x°.

Since there is continuously acceleration due to gravity actjng upon it, and since cylinder is making sime angle with horizontal therefore a component of acceleration due to gravity will act.

If we divide acceleration due to gravity in two components, the component along the line of motion of cylinder would be gsinx.

Now in first case i.e when cylinder is moving upward,

Velocity is positive as it is moving in the direction of velocity and since acceleration due to gravity is acting opposite to the direction of motion it will be NEGATIVE.

when it reaches at the top and turns, here the it is at rest so velocity is ZERO but acceleration due to gravity is still acting on It down the slope or in its direction of motion, so it is positive and had the cylinder not turned it would have been negative.

When it starts rollind down the slope, the velocity and acceleration due to gravity, both are in same direction and Re along the direction of motion, so velocity as well as acceleration are POSITIVE.