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A small ball 'A' of mass 'm' is attached rigidly to the end of a light rod of length 'd'. The structure rotates about an axis perpendicular to the rod and passing through its other end with an angular velocity 'ω'. The angular momentum of the system about this axis is.

A
12mωd2
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B
14mωd2
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C
mωd2
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D
2mωd2
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Solution

The correct option is C mωd2

Angular momentum of A about the axis of rotation,

L=rXp {here rp}
Lrp sin 90=rp

Now, the magnitude of linear momentum of A, which is d units apart from axis of rotation = mv

By Rotational Kinematics, we know clearly,

V=ωr

V=ωd.
L=mωd2 {L=mvr}

Directed along the Axis of Rotation.


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