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  4. A small coin is placed at a distance r from the centre of a gramophone record. The rotational speed of the record is gradually increased. If the coefficient of friction between the coin and the record is μ , the minimum angular frequency of the record, for which the coin will fly off, is given by

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Q. A small coin is placed at a distance $r$ from the centre of a gramophone record. The rotational speed of the record is gradually increased. If the coefficient of friction between the coin and the record is $\mu $ , the minimum angular frequency of the record, for which the coin will fly off, is given by

NTA AbhyasNTA Abhyas 2020Laws of Motion

Solution:

The coin performs circular motion in a circle of radius $r$ . It will fly off when centrifugal force is greater than the centripetal force provided by friction
Hence, at the moment when the coin is about to fly off,
$\mu N=m\omega ^{2}r$
or $\mu mg=m\omega ^{2}r$
$\omega =\sqrt{\frac{\mu g}{r}}$