Consider a situation like a coin slips off a rotating disc due to the lack of static friction. Is the object's angular velocity changed when the centripetal force becomes kinetic friction at the moment that the block hasn't slipped off the disc?
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$\begingroup$ What do you think? Is the object moving with a constant radius if kinetic friction is involved? $\endgroup$– Bill NCommented Mar 5, 2020 at 13:35
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$\begingroup$ If the disc is not hinged and is on a smooth floor : While the block is slipping disc will continue to rotate but with different angular velocity and it will also start doing translational motion about centre of mass...................If disc is hinged : Only its angular velocity will be changed which can be found out by conserving angular momentum $\endgroup$– Mitul AgrawalCommented Mar 5, 2020 at 13:38
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1 Answer
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While the coin is rotating in a circle (ie constant radius) with constant angular velocity, static friction is providing only a radial force (centripetal force). It does not apply any tangential force on the coin because the coin has no tangential acceleration. Its own inertia keeps it moving with a constant speed.
If the coin slips outwards its radius $r$ increases but its tangential speed $v$ remains the same initially, so its angular velocity $\omega=v/r$ decreases.
However, the turntable underneath the coin is still rotating with the same angular velocity as before, so it is sliding forward beneath the coin. There is relative motion tangentially therefore kinetic friction acts to increase the tangential speed $v$ of the coin. If the coin does not slip any further outwards then the angular velocity of the coin increases, approaching that of the turntable. But it is likely that the coin will continue slipping outwards, resulting in a further decrease of its angular velocity.
answered Mar 7, 2020 at 23:52