# Direction of friction in circular motion

• Vatsal Goyal
In summary, friction acts radially inwards on a rotating turntable because there is a centripetal force acting to keep the object moving in a circular path.
Vatsal Goyal

## Homework Statement

I can't understand why friction acts radially inwards when a body is rotating on a rough turntable. If the friction is removed, the body would move tangentially, hence it has slipping tendency tangential, not radially outwards, then shouldn't friction act tangentially?

## The Attempt at a Solution

The idea that friction acts radially inwards seems very counter-intuitive to me. I know that there has to be a centripetal force as the body is in circular motion, and a force is required to balance the centrifugal force, but why is it friction and why wouldn't it act tangentially bugs me.

It would move tangentially because there would be nothing to change its state of motion. In any motion with constant speed, the acceleration is orthogonal to the velocity. Any component of a resultant force that was tangential to the path would accelerate the object.

Vatsal Goyal
Could you help me understand why it is the frictional force that provides centripetal acceleration. I am taught that frictional force acts opposite to the slipping tendency, then why does it act radially inwards if the slipping tendency is tangential.

Vatsal Goyal said:
I am taught that frictional force acts opposite to the slipping tendency,

Correct but the slipping tendency is not tangential...

If it was released it would indeed move tangentially to the circular path it was following BUT it moves more or less radially with respect to the point on the surface where it was previously sitting. So the relative motion, the red line, is radial (for small theta).

PS: It would be tangential if the rotating surface suddenly stopped rotating and the object kept going.

#### Attachments

• Relative motion.jpg
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Vatsal Goyal and haruspex
CWatters said:
the slipping tendency is not tangential...
Just to stress that a bit more, slipping is relative motion of surfaces in contact; friction opposes that relative motion, not motion in the lab frame.
Also, part of your confusion comes from motion in the sense of acceleration versus in the sense of velocity. Without friction, there is no acceleration (in the lab frame) and the velocity is tangential. With static friction, the acceleration is radial and the velocity keeps changing.

Vatsal Goyal and CWatters

## 1. What is the direction of friction in circular motion?

The direction of friction in circular motion is always tangential to the circular path. This means that it is perpendicular to the radius of the circle at any given point on the path.

## 2. How does the direction of friction affect circular motion?

The direction of friction plays a crucial role in circular motion as it provides the necessary centripetal force to keep an object moving in a circular path. Without friction, the object would continue moving in a straight line tangent to the circle.

## 3. Does the direction of friction change throughout the circular motion?

Yes, the direction of friction can change throughout the circular motion. As the object moves along the circular path, the direction of friction will also change to always be perpendicular to the radius of the circle at that point.

## 4. How does the magnitude of friction affect circular motion?

The magnitude of friction can affect circular motion in two ways. If the magnitude of friction is too low, the object may not have enough centripetal force to maintain the circular path and may slide off the path. If the magnitude of friction is too high, it can cause the object to slow down or even stop moving along the circular path.

## 5. How can the direction of friction be altered in circular motion?

The direction of friction can be altered in circular motion by changing the direction of the object's motion or by changing the surface it is moving on. For example, if the object is moving on a curved surface, the direction of friction will change to be perpendicular to the curved surface rather than the radius of the circle.

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