Question:
A child is standing with his two arms outstretched at the centre of a turntable that is rotating about its central axis with an angular speed $\omega_0$ . Now, the child folds his hands back so that moment of inertia becomes $3$ times the initial value. The new angular speed is
A child is standing with his two arms outstretched at the centre of a turntable that is rotating about its central axis with an angular speed $\omega_0$ . Now, the child folds his hands back so that moment of inertia becomes $3$ times the initial value. The new angular speed is
Updated On: Jul 5, 2022
- $3\omega_0$
- $\frac {\omega_0}{3}$
- $6\omega_0$
- $\frac {\omega_0}{6}$
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The Correct Option is B
Solution and Explanation
Here,
Initial angular speed, $\omega_i = \omega_0$
Initial moment of inertia $= I_i$
Final moment of inertia $ I_f = 3I_i$
According to the law of conservation of angular momentum, we get
$L_i = L_f$ or $I_i\omega_i = I_f \omega_f$
$\omega_{f} = \frac{I_{i}\omega_{i}}{I_{f}} = \left(\frac{I_{i}}{I_{f}}\right)\omega_{i} $
$= \left(\frac{I_{i}}{3I_{i}}\right)\omega_{0} = \frac{\omega_{0}}{3}$
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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.