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A rigid rod of mass m & length l is pivo...

A rigid rod of mass m & length l is pivoted at one of its ends. If it is released from its horizontal position, find the speed of the centre of mass of the rod when it becomes vertical.

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To solve the problem of finding the speed of the center of mass of a rigid rod of mass \( m \) and length \( l \) when it becomes vertical after being released from a horizontal position, we can follow these steps: ### Step 1: Understand the System The rod is pivoted at one end and released from a horizontal position. The center of mass of the rod is located at a distance of \( \frac{l}{2} \) from the pivot. ### Step 2: Calculate the Work Done by Gravity When the rod falls from the horizontal to the vertical position, the center of mass drops a vertical distance of \( \frac{l}{2} \). The work done by gravity can be calculated as: \[ ...
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