Direction of friction in circular motion

[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?

Homework Equations

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.

 

[Orodruin]

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.

 

[CWatters]

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.

 

[haruspex]

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]

Thank you so much @CWatters and @haruspex, this makes so much more sense to me now!