Concepts of Physics

IIT JEE Physics (1978-2018: 41 Years) Topic-wise Complete Solutions

Demonstration of Conservation of Angular Momentum

Objective

Showing conservation of angular momentum qualitatively

Introduction

If a particle of mass \(m\) is moving with an angular speed \(\omega\) in a circular path of radius \(r\), its angular momentum about the axis of rotation is \(m\omega r^2\). If the radius \(r\) is decreased in such a way that there is no torque about the axis of rotation, the angular speed will increase to conserve the angular momentum. The quantity \(m\omega r^2\) remain constant. This demo show it in a very clear manner.

Apparatus

A thread, two objects with unequal masses, body of a ball pen

Procedure

Pass a thread through the both side open plastic body of a used ball pen. Tie two unequal masses \(m\) and \(M\) on the two sides of the string. Hold the plastic body in vertical position in your hand with the heavier mass \(M\) hanging and the lighter mass \(m\) resting at the top of the plastic body. Give motion to the masses by rotating your hand little bit. Speed up the rotating lighter mass so that the heavier hanging mass moves right up to the plastic body.

Now, slowly pull the mass \(M\) downward. You will see that other mass starts rotating faster. Why?

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Discussion>

When \(M\) is pulled down, the radius \(r\) is reduced. Thus, to keep the angular momentum \(m\omega r^3\) constant, the angular velocity \(\omega\) increases. Hence, \(m\) starts rotating faster.