Rotation of two motors and two disk with friction

Homework Statement

I changed the problem, because I understood my error I forgot a force. It's the same problem with one motor.

A motor drives two disks on a support. The support is turning clockwise at w1. Disks turn at w at start. The motor M gives a force F and a counterclockwise torque Fd/2 to the red disk. The motor M gives a force F and a counterclockwise torque Fd/2 to the magenta disk. The images shows rings but it's disks. There is friction at points A and B between disks, the force of friction is F/2.

http://imageshack.com/a/img908/4925/N672Ta.png [Broken]

1) Draw all forces
2) Calculate the torque on each disk
3) Calculate the torque on the support

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The Attempt at a Solution

1) I drawn all forces:

http://imageshack.com/a/img540/4338/6D0fx5.png [Broken]

http://imageshack.com/a/img540/7663/cN4A9b.png [Broken]

I noted all forces but:

|F1|=|F2|=|2F3|=|2F4|=|2F5|=|2F6|=|F7|=|F8|=|F|

The color shows where goes the force, magenta -> to the magenta disk, red -> to the red disk, blue -> from the motor M to the support. Prime forces, like F4 -> F4' are forces that must be reported to the axis.

I'm not sure about my forces !

2) Each disk receives a torque +FR/2-F(R-d)/2=Fd/2 from other disk and -Fd/2 from a motor. So the torque on each disk is 0.

3) If my forces are correct there is no torque on the support from disks. But the motor gives a clockwise torque Fd/2, so the support receives a clockwise torque Fd.

Is it correct ?

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haruspex
Homework Helper
Gold Member
|F1|=|F2|=|2F3|
How do you deduce that?

The problem statement said the motor gives F to the red disk and F to the magenta disk. Then I drawn, F1, F2, F7, F8, and I can say |F1|=|F2|=|F7|=|F8|=|F|. I reported forces F1 and F2 to the axis, it gives F1' and F2' with |F1|=|F2|=|F|.

Friction is F/2 between disks at points A and B. Then I drawn F3, F4, F5, F6 and I can say |2F3|=|2F4|=|2F5|=|2F6|=|F|. I reported forces to the axes, it gives F3', F4', F5', F6'.

It is not correct ?

Sorry, I was wrong. The motor gives +Fd/2 torque on the support so each disk receives -Fd/4 not -Fd/2 and centers of rotation of disks were not well placed. But the force of friction was correct. I drawn forces again:

http://imageshack.com/a/img661/4091/cswtaf.png [Broken]

and:

http://imageshack.com/a/img904/545/7qH6am.png [Broken]

2) Each disk receive a torque F/2*R-F/2(R-d)=Fd/2 from the other disk and a torque -Fd/4 from the motor. Then each disk receives a torque Fd/4

3/ The support don't receive a torque from disks but the motor gives a counterclockwise torque -Fd/4 to the support.

Is it correct ?

Last edited by a moderator:
haruspex