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Standard XII

Physics

Angular Analogue of Linear Momentum

A uniform dis...

Question

A uniform disc of mass $m$ radius $R$ translating with a speed $v$ on a smooth horizontal table is hinged at one point on the circumference all of a sudden. The angular velocity of the disc is

\frac{2 v}{R}

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\frac{v}{3 R}

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\frac{2 v}{3 R}

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Solution

The correct option is C $\frac{2 v}{3 R}$
Apply conservation of angular momentum about the fixed point.
$m v R = [\frac{m R^{2}}{2} + m R^{2}] ω$
$ω = \frac{2 v}{3 R}$

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A uniform disc of mass m radius R translating with a speed v on a smooth horizontal table is hinged at one point on the circumference all of a sudden. The angular velocity of the disc is

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A uniform disc of mass $m$ radius $R$ translating with a speed $v$ on a smooth horizontal table is hinged at one point on the circumference all of a sudden. The angular velocity of the disc is

The correct option is C $\frac{2 v}{3 R}$
Apply conservation of angular momentum about the fixed point.
$m v R = [\frac{m R^{2}}{2} + m R^{2}] ω$
$ω = \frac{2 v}{3 R}$