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) $3 \omega_{0}$ (b) $\frac{\omega_{0}}{3}$ (c) $6(1)_{0}$ (d) $\frac{\omega_{0}}{6}$

Name: Problem 75, Chapter 7: Objective NCERT at your FINGERTIPS: Physics
Uploaded: 2021-09-28T14:35:42-08:00
Duration: 1 min 43 s
Channel: Dheeraj Sharma
Description: 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 ω0. Now, the child folds his hands back so that moment of inertia becomes 3 times the initial value. The new angular speed is (a) 3 ω0 (b) (ω0)/(3) (c) 6(1)0 (d) (ω0)/(6)

   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) $3 \omega_{0}$
(b) $\frac{\omega_{0}}{3}$
(c) $6(1)_{0}$
(d) $\frac{\omega_{0}}{6}$

Objective NCERT at your FINGERTIPS: Physics

NCERT 11th Edition

Chapter 7, Problem 75

Instant Answer

Solved by Expert Dheeraj Sharma

09/28/2021

Step 1

The initial angular speed is $\omega_{1} = \omega_{0}$ and the initial moment of inertia is $I_{1} = I$. The final moment of inertia is $I_{2} = 3I$. Show more…

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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) $3 \omega_{0}$ (b) $\frac{\omega_{0}}{3}$ (c) $6(1)_{0}$ (d) $\frac{\omega_{0}}{6}$

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Key Concepts

Angular Momentum Conservation

This principle states that in the absence of external torques, the total angular momentum of a system remains constant. When the moment of inertia of the system changes, such as when the child folds his arms, the angular speed adjusts to maintain the constant angular momentum, leading to an inverse relationship between angular speed and moment of inertia.

Moment of Inertia

Moment of inertia is a physical quantity that represents how mass is distributed relative to the axis of rotation. It determines the resistance of an object or system to changes in its rotational motion. In systems where the configuration changes, such as moving arms inward or outward, the moment of inertia changes and consequently affects the angular speed to conserve angular momentum.

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