Question

If a body is rotating about an axis passing through its centre of mass, the angular momentum of the body is directed along its

• A. Circumference
• B. Radius
• C. Axis of rotation
• D. None of the above

Answer 1

Answer: (C)

Axis of rotation

Answer 2

The angular momentum ($\vec{L}$) of a rigid body rotating about an axis is given by the product of its moment of inertia ($I$) and its angular velocity ($\vec{\omega}$):

$\vec{L} = I\vec{\omega}$

Moment of inertia ($I$) is a scalar quantity. Angular velocity ($\vec{\omega}$) is a vector quantity whose direction is along the axis of rotation, determined by the right-hand rule.

Since $\vec{L}$ is the product of a scalar ($I$) and a vector ($\vec{\omega}$), the direction of $\vec{L}$ will be the same as the direction of $\vec{\omega}$. Therefore, the angular momentum of the body is directed along its axis of rotation.