First slide

General Planar motion

Question

A conical pendulum consists of a simple pendulum moving in a horizontal circle as shown in the figure. C is the pivot, O is the center of the circle in which the pendulum bob moves and $ω$ is the constant angular velocity of the bob . If $\vec{L}$ is the angular momentum about point C, then

Moderate

A

$\vec{L}$ is constant
B

only direction of $\vec{L}$ is constant
C

only magnitude of $\vec{L}$ is constant
D

none of the above

Solution

Method-1:The distance of $\vec{L}$ is perpendicular to the line joining the bob at point C. Since this line keeps changing its orientation in space, direction of $\vec{L}$ keeps changing, however, as $ω$ is constant, magnitude of $\vec{L}$ remains constant.
Method-2: The torque about point is perpendicular to the angular momentum vector about point C. Hence it can only change the direction of $\vec{L}$ and not its magnitude.

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