Motion of a particle on a rotating frictionless turntable

I hate this question. If there is no friction the particle has no forces acting on it so why does it move at all?

What do others think?

 

Yes.

So it's stationary w.r.t the ground.

I'll let you describe how the particle moves w.r.t the turntable.

 

If the observer not on the center, then he is in a non-inertial frame.

 

Yes, it is right.

ehild

 

Without friction, the particle placed on the rotating table would stay at the same position, and the table turns round under it.

Friction acts between surfaces in contact and tends to hinder the relative motion. When you put the particle on the turntable, the particle moves along a circle with respect to the table, the relative velocity is tangential in the first instant so the force of friction is tangential and the particle starts to move along the tangent of the circle. But its gets a bit further from the centre in the next instant, so the force of friction will have also radial component toward the centre. If the friction is strong enough sooner or later the particle will rotate together with the table. The circular motion it performs needs the centripetal force. It is provided by the force of friction, that points inward.

ehild

 

Hi Tania, I tried to do my best, and draw a picture for you .
It is what an observer sees from outside.

The turntable rotates clockwise, a particle is placed on it (the blue dot). It is initially rest with respect to the observer. Vt is the linear velocity of the point of the table where the particle is placed. The relative velocity is -Vt, the force of kinetic friction is opposite to the relative velocity, it accelerates the particle to the right, it gains some velocity to the right, while the table turns. We arrived to the second picture. The particle moved a bit farther from the center and has velocity Vp. The linear velocity of the table at that point is Vt. The relative velocity is the vector difference Vp-Vt. It is shown in green. The kinetic friction is opposite, and it has both tangential and radial components. It accelerates the particle, it shifts, and so on, while the particle gains velocity equal with the table. If the relative velocity is zero, static friction acts between them and it must be radial and equal to the centripetal force to keep the particle moving together with the table, that is, to be in rest relative to the table.

ehild

 

It means the particle moves radially to, so the friction will have radial component besides the tangential one.

ehild

 

Sorry, I can not. Remember, friction opposes relative motion. It explains everything. What is you do not understand yet?

ehild