Coin on Gramophone Record – Rankers Physics

Dynamics of Circular Motion: Practice Problem & Solution

A gramophone record is revolving with an angular velocity \( \omega \). A coin is placed at a distance \( r \) from the center of the record. The static coefficient of friction is \( \mu \). The coin will revolve with the record if: (2010 Pre)
\( r \ge \frac{\mu g}{\omega^2} \)
\( r = \mu \omega^2 \)
\( r < \frac{\omega^2}{\mu g} \)
\( r \le \frac{\mu g}{\omega^2} \)

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Dynamics of Circular Motion. Understanding the underlying formula is key to arriving at the correct answer below:

For the coin to revolve without slipping, the static friction must provide the necessary centripetal force. Required centripetal force \( F_{\text{c}} = mr\omega^2 \). Maximum static friction \( f_{\text{s,max}} = \mu mg \). So, \( mr\omega^2 \le \mu mg \). This simplifies to \( r\omega^2 \le \mu g \), or \( r \le \frac{\mu g}{\omega^2} \).

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