How Does Friction Affect a Rotating Disk on an Inclined Plane?

[mmainak]

Actually I am a bit confused with the direction of the frictional force acting on a rotating disk on an inclined plane.

I need to find the direction of frictional force on the rotating disk both the cases when it is going up and coming down under the action of an impulsive force applied on it which made it climb through a distance along the inclined plane.

The Attempt at a Solution

In my knowledge, if no friction acting in between them the disk would simply rotate at the same place. When we apply friction it's free rotation is obstructed and it will move on the plane while the friction is actually acting in direction of its motion.

So for a rotating disk friction acts along the motion.
But when I check the answer of the problem it is given that while it is going up the friction will act opposite to it's motion to decrease it's angular momentum.


I need a bit clarification in this regard.

 

[kuruman]

The drawing you posted is misleading. Frictional force (or any other force for that matter) does not increase or decrease angular velocity. You need a torque to change the angular velocity. The net torque about the cylinder axis is out of the screen regardless of whether the cylinder is rolling up or down hill.

I think that you are confusing static friction (what you have in this case) with kinetic friction. Kinetic friction opposes the motion but static friction is in whatever direction is necessary to provide the observed acceleration.

 

[mmainak]

why then rotation of the disk decreases and stops at a time while it crawls up? As you said, rotating body doesn't change the angular momentum of its own, only if some external torque applied on it .Which force is supplying this torque??

 

[kuruman]

If you calculate the torque about the point of contact, the only force that produces a torque is the weight. If you calculate the torque about the center of the cylinder, the only force that produces a torque is static friction.

Regardless of which of the two you pick, the torque will be out of the screen and so will the angular acceleration.

If the angular velocity is also out of the screen, this means that the cylinder is rolling down hill (counterclockwise). The speed will be increasing because the angular acceleration and the angular velocity are in the same direction.

If the angular velocity is into the screen, this means that the cylinder is rolling up hill (clockwise). The speed will be decreasing because the angular acceleration and the angular velocity are in opposite directions.

 

[rwisz]

I can provide an explanation for the direction of frictional force acting on a rotating disk on an inclined plane. The direction of frictional force is dependent on the relative motion between the disk and the inclined plane.

When the disk is moving up the inclined plane, the frictional force acts in the opposite direction of its motion, as stated in the answer to the problem. This is because the disk is moving against the direction of gravity, and the frictional force helps to counteract the downward force of gravity, allowing the disk to move up the plane.

On the other hand, when the disk is moving down the inclined plane, the frictional force acts in the same direction as its motion. This is because the disk is now moving in the same direction as the force of gravity, and the frictional force helps to slow down the disk's motion and prevent it from accelerating too quickly.

In both cases, the frictional force is acting in the direction that helps to maintain the disk's motion and prevent it from slipping or sliding on the inclined plane. It is important to note that the direction of frictional force is always opposite to the direction of motion, regardless of whether the motion is up or down the inclined plane.

I hope this explanation clarifies any confusion you may have had about the direction of frictional force on a rotating disk on an inclined plane. If you have any further questions, please do not hesitate to ask.