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### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# Gyroscopes used in guidance systems to indicate directions in space must have an angular momentum that does not change in direction. Yet they are often subjected to large forces and accelerations. How can the direction of their angular momentum be constant when they are accelerated?

The direction of the angular momentum of the gyroscope is constant because it is perpendicular to the applied torque.

See the step by step solution

## Step 1: Angular momentum

The mass, rotation, and speed of an object, as well as the radius of the object, determine its angular momentum.

## Step 2: Describe what a gyroscope is.

A gyroscope is a device that helps determine the direction in space. It comprises of a disc mounted on the base that may easily move in different directions while maintaining the orientation regardless of movement in the space. It operates on the angular momentum conservation principle.

## Step 3: Describe the direction of angular momentum.

The torque on the disc in the gyroscope produces angular momentum, which causes precession in the wheel. The torque and angular momentum are related as follows:

$T=\frac{△L}{△t}$

Here, T is the net torque, $△L$ is the change in momentum and $△t$ is the change in time. So, the direction of change in angular momentum is the same as that of torque.

When a body gets accelerated, there will be a torque and it will cause a change in angular momentum, which is in a direction perpendicular to the angular momentum.

So, the direction of angular momentum is constant in the gyroscope.