00:01
So here we have the top view, the side view, and the free body diagram before tension comes into play.
00:06
So as the turntable speeds up from rest, we know that the static frictional force provides the centripetal force, and no tension is built into the string for a certain amount of time.
00:19
We can say that then at some critical value omega sub 1, we'll say, the static friction force reaches its maximum value.
00:29
So we can say then that the force of friction would be equal to this critical value in use of smg.
00:41
And essentially we have mv squared over r, the mass times the centriple acceleration, equaling the mass multiplied by omega sub 1 squared, multiplied by r, equalling the coefficient of static friction, mg.
00:58
To find that critical value, omega sub 1, this would be equal to the square root of this coefficient of static friction, multiplied by g divided by r.
01:11
And in this case, once the angular velocity exceeds this value, omega sub 1, static friction isn't enough to provide the centripetal force that is required to keep it moving.
01:26
So now attention does exist, and that's what this free body diagram here is presenting.
01:35
So here we can say that first, omega sub 2, we know to be 60 rpm's, and we'll multiply this by 2 pi radians for every revolution, and we'll multiply this one minute for every 60 seconds.
01:55
And so omega sub 2 is going to be equaling then 2 .00 pi radians per second...