Question:

A uniform rod $AB$ of length $l$ and mass $m$ is free to rotate about point $A$. The rod is released from rest in the horizontal position. Given that the moment of inertia of the rod about $A$ is $\frac{ml^2}{3}$ the initial angular acceleration of the rod will be

Updated On: Jul 5, 2022
  • $\frac{2g}{3l}$
  • $\frac{mgl}{2}$
  • $\frac{3gl}{2}$
  • $\frac{3g}{2l}$
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The Correct Option is D

Solution and Explanation

Torque about $A$ $\tau=mg \frac{l}{2}$ also, $\tau=I \alpha$ Angular acceleration $\alpha=\frac{\tau}{I}=\frac{mgl /2}{ml^{2}/ 3}=\frac{3g}{2l}$ ${\text{(Given}} \, I=\frac{ml^{2}}{3})$
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Notes on rotational motion

Concepts Used:

Rotational Motion

Rotational motion can be defined as the motion of an object around a circular path, in a fixed orbit.

Rotational Motion Examples:

The wheel or rotor of a motor, which appears in rotation motion problems, is a common example of the rotational motion of a rigid body.

Other examples:

  • Moving by Bus
  • Sailing of Boat
  • Dog walking
  • A person shaking the plant.
  • A stone falls straight at the surface of the earth.
  • Movement of a coin over a carrom board 

Types of Motion involving Rotation:

  1. Rotation about a fixed axis (Pure rotation)
  2. Rotation about an axis of rotation (Combined translational and rotational motion)
  3. Rotation about an axis in the rotation (rotating axis)