Originally Posted by **alexito01** 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