Welcome to Ichiro Takeda's homepage

Why a spinning top does not fall over?

Why a spinning top does not fall over?

It seems that there is no plain explanation although everyone has a question about this.
However, if it explains as follows, it will be able to be made clear to almost all persons.

For understanding the principle, the assumptions of Newtonian mechanics is very useful for us.

(1) If force is not applied, a particle continues to move at a constant speed along a straight line.
(2) If force is applied to a particle, acceleration will occur according to the force.
Newtonfs second law of motion can be written in the simplified form
Where F: force, m: mass of the rigid body and : acceleration on it.

This theory can be applied to rotating rigid body:
(1) The body will continue rotation if a couple is not applied to it;
(2) If a couple is applied on a rigid body, speed of rotation will change according to it.

What is a couple?

A couple is defined in mechanics such as two equal and parallel forces with each opposite direction.
The forces have a turning effect or moment called a torque.

An introduction is finished and goes into main subject.

Suppose that a sphere is rotating now in a place like in the space.

 Please imagine the earth is turning around in the space.

An axis of rotation is also attached to this rotating sphere.

Moreover two points on the equator are added as seen on a figure.

 When one point comes to the front, the lower end of an axis is fixed and a force is applied to the upper end of the axis in a very short time.

Let us consider the movement of these two points after the operation.

By having pushed the upper part, rotation of a top changes from the left Figure to the right one.

Fig.5 shows a side view of these spheres.

This means that the axis of rotation begins to move towards the left to the right angle from the pushed one.

Such a phenomenon is called "gyroscope effect."

If the top is turning, gravity will carry out the force which is going to push down it.

As a result, an axis moves to the right angled direction, and upper part of axis turns around on the circle shown in the Fig. 7.

This is called precession movement.

The explanation is over

In Japanese home page, many interesting figures are shown.

Japanese Homepage