A 5.0 g coin is placed 15 cm from the center of a turntable. The coin has static and kinetic coefficients of friction with the turntable surface of . The turntable very slowly speeds up to 60 rpm. Does the coin slide off?
Solution Step 1 of 5 Centripetal force is the force that acts on a body which is moving in the circular path and it is directed towards the center of the circular path on which the body is moving, as in the figure below;here as the coin on the turntable is rotating Centripetal force(F) of coin under uniform circular motion is given by equation F =cm r2 Where m and are the mass and angular velocity of the coin, r is the radius. Step 2 of 5 Static friction is the opposition offered for the applied force on an object, to keep the object at rest. At the start, when we push a block, we experience an opposition that is offered by static frictional force. Once the static frictional force is overcome, then we experience kinetic friction in motion. When the coin is on the turntable is rotating the centripetal force will be due to the static force that is acting on the coin, due to the instantaneous contact of coin with the turntable, because which there will be no sliding or skidding of coin during turning of table. The Static friction is given by, F s mgs Where coesficient of static friction, m is the mass and g is the acceleration due to gravity. Step 3 of 5 The condition for skidding of the coin on the turntable is, when the centripetal force on the coin becomes equal to the maximum static friction. Thats is Centripetal force(F )= scatic frictional force(F ) Using above equations, F =F s c 2 smg=m r 2 sg= r