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# Rotating frame of reference

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A coin stands upright at an arbitrary point on a rotating turntable, and
spins (without slipping) at the required angular speed to make its center
remain motionless in the lab frame. In the frame of the turntable,
the coin rolls around in a circle with the same frequency as that of the
turntable. In the frame of the turntable, show that
(a) F = dp/dt, and
(b) τ = dL/dt (Hint: Coriolis).

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#### Solution Preview

A coin stands upright at an arbitrary point on a rotating turntable, and spins (without slipping) at the required angular speed to make its center remain motionless in the lab frame. In the frame of the turntable, the coin rolls around in a circle with the same frequency as that of the turntable. In the frame of the turntable, show that
(a) F = dp/dt, and
(b) τ = dL/dt (Hint: Coriolis).
(a) If the frame of reference is fixed with the turntable, the center of mass of the coin appears to rotate in a circle with angular velocity  same as that of the turn table. If the mass of the coin be m and the radial distance from the axis of rotation is R than we have to consider pseudo force acting on the coin which is providing the necessary centripetal force equal to m2R acting radially inward. This will be the net force acting on the coin in the frame of the ...

#### Solution Summary

A coin is spinning on a turntable in such a way that remain in equilibrium in the lab frame. Newton's laws are proved in the frame of the turntable using pseudo force.

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