A uniform rod of length is pivoted at one of its ends on a vertical shaft of negligible radius. When the shaft rotates at angular speed the rod makes an angle with it (see figure). To find equate the rate of change of angular momentum (direction going into the paper) about the centre of mass (CM) to the torque provided by the horizontal and vertical forces and about the CM. The value of is then such that:
Step 1. Given data:
A uniform rod of length
Angular speed is and the rod makes an angle
The rate of change of angular momentum equals torque
Step 2. solving for :
From the diagram,
The horizontal force is,
The vertical force is,
Where is the acceleration due to gravity
The net torque about the centre of mass is,
Equating equation and , we get
Hence, option B is correct.