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

# Gyroscope from Cycle Wheel

## Introduction

It is a common experience that a bicycle can be parked only when we support it with a stand otherwise it will fall down. But the same bicycle when moving on the road can be balanced very well on its two wheels. Wheels of a moving bicycle have a very large spin angular momentum which helps in maintaining the balance of the bicycle. This is the basic principle of a gyroscope. In this demonstration we will see how a spinning cycle wheel is affected by external torque.

## Apparatus

A cycle wheel with an axle, rope

## Procedure

1. Attach a rope to the axle of the cycle wheel.
2. Hold the cycle wheel by the rope. See that the wheel topples down.
3. Hold the cycle wheel from its axle and give it a spin in clockwise direction.
4. When the wheel acquires a large angular velocity, leave the axle and hold the wheel by the rope attached to the axle.
5. See that the wheel instead of toppling this time starts présession around the rope in the anticlockwise direction when seen from above.
6. Now hold the cycle wheel from the axle, spin it in anticlockwise direction, and again hold it with the rope but this time see that the wheel précess in a clockwise direction around the rope.
7. When the wheel is held by the rope, (i) why does it topple when it is not spinning and (ii) why does it start precession when it is spinning?

## Discussion

When we hold the cycle wheel by the rope attached to the axle, the tension in the rope and the weight of cycle wheel acting through the centre of mass of the wheel cause a torque which topples the wheel. A spinning wheel has a spin angular momentum $$\vec{L}$$, whose direction is given by the right hand thumb rule. If you spin it in clockwise direction, the spin angular momentum $$\vec{L}$$ is away from you and perpendicular to the plane of the wheel. If you spin it in anticlockwise direction, $$\vec{L}$$ is towards you. If the angular velocity is large, $$\vec{L}$$ is also very large.

Now, when a torque is applied by holding the rope, the torque acts in a direction perpendicular to $$\vec{L}$$. This causes an additional small angular momentum $$\mathrm{d}\vec{L}$$ in the direction of the torque. The net angular momentum is now the vector sum of $$\vec{L}$$ and $$\mathrm{d}\vec{L}$$ which is no more perpendicular to the plane of the wheel but is slightly tilted towards the applied torque. This causes the angular momentum $$\vec{L}$$ to follow the torque and the wheel starts precession about the rope.

Reversing the direction of angular momentum $$L$$ causes the wheel to precess in an opposite sense.