Question:
The angular speed of a body changes from $\omega_1$ to $ \omega_2$ without applying a torque, but due to change in moment of inertia. The ratio of radii of gyration in the two cases is
The angular speed of a body changes from $\omega_1$ to $ \omega_2$ without applying a torque, but due to change in moment of inertia. The ratio of radii of gyration in the two cases is
Updated On: Jul 5, 2022
- $\sqrt{\omega_1}:\sqrt{\omega_2}$
- $\sqrt{\omega_2}:\sqrt{\omega_1}$
- $\omega_2:\omega_1$
- $\omega_1:\omega_2$
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The Correct Option is B
Solution and Explanation
In the absence of external torque
$I_1 \omega_1=I_2 \,\omega_2$
or $MK^2_1\,\omega_1=MK^2_2\, \omega_2$
$=\frac{K_1}{K_2}=\sqrt{\frac{\omega_2}{\omega_1}}$
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Concepts Used:
System of Particles and Rotational Motion
- The system of particles refers to the extended body which is considered a rigid body most of the time for simple or easy understanding. A rigid body is a body with a perfectly definite and unchangeable shape.
- The distance between the pair of particles in such a body does not replace or alter. Rotational motion can be described as the motion of a rigid body originates in such a manner that all of its particles move in a circle about an axis with a common angular velocity.
- The few common examples of rotational motion are the motion of the blade of a windmill and periodic motion.