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Old Oct 14th 2008, 10:22 PM   #1
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help with angular acceleration prob

heres the problem:

A penny rests on a record at a radius of r=0.200m. The record player is turned on and the record steadily accelerates with angular acceleration alpha = 20.0 rad/s^2. The coefficient of static friction between the record and the penny is 0.500. At what time will the penny begin to slip?
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Old Oct 15th 2008, 10:30 AM   #2
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Originally Posted by alexito01 View Post
heres the problem:

A penny rests on a record at a radius of r=0.200m. The record player is turned on and the record steadily accelerates with angular acceleration alpha = 20.0 rad/s^2. The coefficient of static friction between the record and the penny is 0.500. At what time will the penny begin to slip?
Note that you are looking for the maximum force provided by static friction, so we have that $\displaystyle f = \mu _s N$.

So set up a Free Body Diagram that is good for an instant with the positive direction (+r) in the direction of the center of the turn-table. You will easily see that the friction force will be equal to the centripetal force. Thus we have that
$\displaystyle \sum F = f = \mu _s N$
and
$\displaystyle \sum F = F_C = \frac{mv^2}{r}$

Equating these gives
$\displaystyle v = \sqrt{\mu _s gr}$

Now, v is the linear speed of the penny so we know that $\displaystyle v = r \omega$
where $\displaystyle \omega$ is the angular speed just as the penny starts to slip.

So the second part of this problem is finding how long it takes the penny to reach $\displaystyle \omega$. This part I leave to you. If you have further questions, please feel free to let us know.

-Dan
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