# To study the theorem of perpendicular axes in Moment of Inertia

## Objective

To study the theorem of perpendicular axes in Moment of Inertia.

## Introduction

For planer bodies, the sum of the moments of inertia about two axes, perpendicular to each other but in the plane of the body, equals the moment of inertia of the body about the axis through the same point perpendicular to the plane.

The moment of inertia of an object can be found by suspending it from a support and allowing it to oscillate about the suspension. The time period happens to be proportional to the square root of the moment of inertia, \(T=k\sqrt{I}\).

## Apparatus

A wooden plate with two bolts fixed on the sides and one bolt fixed at the center, a wire fixed with a nut, clamp-stand, stop watch.

## Procedure

- Suspend the plate by fixing the bolt in a nut on a side. Let the plate be suspended . Now twist the plate about the vertical axis and measure time period using stop watch. Make sufficient number of readings to be sure of the value. This gives moment of inertia \(I_x\) up to the proportionality constant.
- Open the nut and screw it in the bolt on other side. Get the time period of twist oscillations. From this find the moment of inertia \(I_y\) up to the proportionality constant.
- Again open the nut and screw it in the bolt at the center of the plate. Get the time period of twist oscillations. From this find the moment of inertia \(I_z\) up to the proportionality constant.
- Find the value of \(({I_x+I_y})/{I_z}\).