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Static Friction And A Rotating Platform

Following on from the “Coin in a Glass”, checkers and baskets on a trolley videos, we have this video which brings in another complicating aspect. Again the mass of the object on the rotating plate is not a factor in determining when the object starts to slip. The coefficient of friction is the same for both objects so they will both have a maximum acceleration that can to be provided by friction. So why do they start to slip at different times? Because there are now two acceleration components to consider, centripetal and tangential. And the total acceleration required to be provided by friction is the square root of the sum of the squares.

Let us look at each of these accelerations and see how it changes with distance for a constant angular acceleration. The tangential acceleration of the mass furthest from the point of rotation is directly proportional to the distance from the point of rotation so for a large angular acceleration it will require the largest tangential acceleration to stay on the plate and therefore will reach the limit set by the maximum frictional force first.

If however we keep the angular acceleration constant and small then this is not the determining factor. But the masses will still at some stage come off the plate. The reason for this is that the centripetal acceleration needed for the mass to stay on the plate increases with the square of the angular velocity times the radius. Now both masses have the same angular velocity at all times even though it is increasing, so they will both slip off eventually, but the mass that is at a greater distance from the point of rotation, having the greater radius and therefore the greater tangential velocity, will reach the limiting value set by the maximum frictional force first.

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