00:01
For this problem, we're told we have a coin with a mass of 5 grams or 5 times 10 to the negative 3 kilograms.
00:13
It's placed a distance 15 centimeters from the center of the turntable, or 0 .15 meters.
00:24
And we're told that there is static and kinetic friction between the point in the turntable with the coefficient of static friction being 0 .8 and the coefficient of kinetic friction being 0 .5.
00:41
In part a, we're asked, what is the maximum tangential velocity that the point can withstand without sliding off of the turntable? in order to figure this out, we're going to use newton's second law in the radial direction, which says that the sum of the forces in the radial direction must be equal to mass times the centripetal acceleration, which is v squared over r.
01:07
And the radial direction, if we were to draw a free body diagram for a coin, the only force that will be acting on it will be the force of friction.
01:21
And so we've got our force of friction in that direction.
01:27
If we're looking for the maximum velocity, that's going to be the velocity when we're at our maximum friction force, which will be the maximum static friction.
01:40
And that, of course, has to be in v squared over our.
01:43
Maximum static friction is coefficient of static friction times the normal force.
01:50
And in this problem, because there are no other forces, acting, other than gravity in the normal force, the normal force must be equal to the equal in magnitude to the gravitational force, so it's just going to be mg...