A 100g mass is on a circular turntable spinning at 78 revolutions per minute. The maximum frictional force between the mass and turntable is 0.50N. Find the maximum distance from the center of the turntable at which the mass would stay on the turntable.

First, draw a diagram as it makes the problem easier to understand. Show the turntable and mass. Label the distance between the mass and the centre of the turntable r as it is a radius. write down all variables converting to SI units as it makes it simpler later on, the 100g to 0.1kg, and the 78 rev/min radians/s with this calculation w (angular velocity) = 2xPixfrequency = 2xPix(78/60) = 8.17rad/s. Then equate forces, as because the mass isn't slipping on the disk and is moving at a constant angular velocity they must be balanced. (can draw a 2nd diagram) equate the frictional force to the centripetal force F(friction) = mw^2r. looking up equations on formula sheet if you don't know them. rearrange and substitute in the values giving r = 0.5/(0.1 x 8.17^2) = 7.494x10^(-2) = 7.5x10^(-2) to 2 s.f as values in the question are given to 2s.f ie: 78, 0.50