A layer of mud is placed on a plate. The plate is rotated and the mud near the edge will leave the plate first compare to the mud near the centre when angular speed of the plate is slowly increased. Why is it when centripetal force increases due to the increase in radius, the mud at the edge will leave the surface first?
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Why is it when centripetal force increases due to the increase in radius, the mud at the edge will leave the surface first?
The only significant centripetal force here is the molecular bonding in the material of the plate which keeps it from flying apart as you spin it. This necessarily increases with radius, because the outer edge requires a higher acceleration to maintain the same angular velocity compared to an inner portion of the plate.
The mud sticks slightly to the plate but is not strongly attached to it. When you spin the plate, the plate imparts a tangential acceleration to the mud over it. The mud begins moving in that direction, but there's nothing to "pull" it back onto the plate, so it slides off. The mud at the outside edge is flung off quicker than mud near the center because the tangential linear velocity is higher at a larger radius, so it escapes the plate at a higher rate.