A bob of mass m attached to an inextensible string of length l is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed ω rad/s about the vertical. About the point of suspension: (a) angular momentum is conserved (b) angular momentum changes in magnitude but not in direction. (c) angular momentum changes in direction but not in magnitude. (d) angular momentum changes both in direction and magnitude.

Answer: (c). About the point of suspension, L=m r× v with | r|=l, v⊥ r, so | L|=mlv is constant. L is perpendicular to the string, which keeps turning, so the direction of L changes (torque of gravity is not zero about this point). So the answer is (c).

A bob of mass m attached to an inextensible string of length l is… | JEE Main 2014

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Angular Momentum & its Conservation

A bob of mass $m$ attached to an inextensible string of length $l$ is suspended from a vertical support. The bob rotates in a horizontal circle with an angular speed $\omega\, rad/s$ about the vertical. About the point of suspension:

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Answer: (c)

About the point of suspension, $\vec L=m\vec r\times\vec v$ with $|\vec r|=l$ , $\vec v\perp\vec r$ , so $|\vec L|=mlv$ is constant.
$\vec L$ is perpendicular to the string, which keeps turning, so the direction of $\vec L$ changes (torque of gravity is not zero about this point).
So the answer is (c).

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