Question:
If the radius of earth shrinks by 0.2% without change in its mass, the % change in its angular velocity is
If the radius of earth shrinks by 0.2% without change in its mass, the % change in its angular velocity is
Updated On: Sep 25, 2024
- increases by 0.4%
- increases by 0.1 %
- decreases by 0.4%
- increases by 0.2 %
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The Correct Option is A
Solution and Explanation
$I_{\omega} = \frac{2}{5} MR^2 \omega$ = Constant
$\omega \, \propto \, R^{-2}$ and $\frac{\Delta \omega}{\omega} = -2 \frac{\Delta R}{R}$
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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:
- Rotation about a fixed axis (Pure rotation)
- Rotation about an axis of rotation (Combined translational and rotational motion)
- Rotation about an axis in the rotation (rotating axis)