Two disks (moment of inertia)

  • Thread starter amcavoy
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  • #1
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A uniform circular disk of radius R = 0.200 m and mass M = 1.00 kg rotates with angular speed wo = 10.0 radians/second on a frictionless pivot. A second disk, having half the radius of the first and made of the same material, is supported at rest a small distance above the first disk. When the small disk is dropped concentrically onto the larger disk, friction eventually causes the disks to reach a common angular speed.
What is the final angular speed?

I came up with 9.4 rad/s, which is correct.

What fraction of the initial rotational kinetic energy is converted to heat in the process?

I came up with .0588, which is also correct.

A motor must restore the angular speed of the combination to wo in one revolution. What torque must the motor supply ?

I used the equation [itex]\tau=I\alpha[/itex] here. I added each moment of inertia (for each disk individually):

[tex]I=I_1+I_2=.02125[/tex]

The above I got using the standard formula for the moment of inertia for a disk (1/2)mr2.

Now I found the acceleration:

[tex]10^2=9.4^2+2\alpha\left(2\pi\right)\implies\alpha=.926\text{rad}/\text{sec}^2[/tex]

Then I multiplied the acceleration by the moment of inertia to come up with:

[tex]\tau=.0197\text{Nm}[/tex]

...however the above is incorrect. Could someone please tell me why? I have gone through my steps many times, meaning that the only way this could be wrong is if I took the wrong steps; my arithmetic is fine. I'd appreciate any input on this.

Thank you very much.
 

Answers and Replies

  • #2
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your procedure is correct ... your final solution for tau does have some round-off error in it from rounding the final omega from the 1st part of the problem ... 9.4 rad/s.

If you don't round, you should get tau = .0913092394 Nm

If this is an on-line problem that is machine graded, that could be the reason.
 
  • #3
665
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Thank you very much. It's nice to know my problem was in rounding digits rather than my procedure (it is web-based hw by the way).

Thanks again.
 

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