Motion of a particle on a rotating frictionless turntable

[Tanya Sharma]

Homework Statement

1 A particle is gently placed on a frictionless rotating turntable at a distance r from the centre.Describe particle motion from both ground and table frame.

2 A particle is at a distance r from the centre of a frictionless stationary turntable.The turntable then starts rotating. Describe particle motion from both ground and table frame.

Homework Equations

The Attempt at a Solution

If sufficient friction is present then the particle will also rotate with same angular velocity.But I am not sure what if the surface is frictionless.Are the two cases same or different?Please help...

 

[CWatters]

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?

 

[Tanya Sharma]

I apolozise for making u hate...i agree with ur opinion...does that mean the turntable just slips underneath the particle in both the cases ??

 

[CWatters]

Yes.

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

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

 

[Tanya Sharma]

Does an observer on the turntable sees the particle rotating with same angular velocity as that of the turntable but in opposite direction... i.e if turntable rotates clockwise then to an observer on the turntable particle seems to rotate anticlockwise ?? Please reply

 

[azizlwl]

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

 

[ehild]

Does an observer on the turntable sees the particle rotating with same angular velocity as that of the turntable but in opposite direction... i.e if turntable rotates clockwise then to an observer on the turntable particle seems to rotate anticlockwise ?? Please reply

Yes, it is right.

ehild

 

[Tanya Sharma]

echild ...sir... please clear my doubt ...from reference frame of ground if we see a particle being placed on a rotating table with friction then the particle has a tendency to slip tangentially ... so the friction should act tangentially to the particle...why then does it act towards the centre...please explain w.r .t inertial frame ... thanks

 

[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

 

[Tanya Sharma]

Awesome insight...havent found this anywhere in textbooks...thanks sir...can u suggest from where i can read more about this ...books or web?? So initially the friction is tangential...but after that is it completely radial or has both radial and tangential components ?? Please reply...thanks

 

[Tanya Sharma]

echild ... sir... if possible ...can u explain diagramatically?? thanks

 

[Tanya Sharma]

"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."

need more insight regarding this...

 

[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

 

[ehild]

"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."

need more insight regarding this...

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

ehild

 

[Tanya Sharma]

Sir...i have no words to express my gratitude...thanks a ton... can u suggest from where i can read more about it? more detailed analysis on circular motion and friction...

 

[ehild]

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

ehild

 

[Tanya Sharma]

Sir...what u have explained couldn't have been explained better ...thank u very much...superb explanation!