Introduction

Momentum describes how strong a moving thing is: the heavier and faster something is, the more momentum it has.

It is because of momentum that a planet or a star will move in the same direction unless something happens to push it in another direction. One way to think about momentum is that it measures how hard it will be to stop an object. For example, it is really hard to stop a car rolling down a hill towards you because it is so large (mass). A car going fast will be even harder to stop because it is travelling at speed (velocity).

The key thing to remember here is:

Momentum = Mass x Velocity (speed)

A special type of momentum is ‘Angular Momentum’. This is when an object spins around like a spinning top instead of going straight like the car. Think of a basketball player spinning the ball on his finger:

                                             

Spinning objects also behave differently to stationary objects: the greater the angular momentum of an object, the greater its resistance to any turning force (called a ‘moment’) acting upon it. This can be demonstrated with a spinning top. Release a stationary spinning top and it will topple over. Release a spinning top with a certain angular momentum and it will remain upright while spinning.

The greater the radius, mass and/or velocity of a rotating object, the greater its angular momentum.

Our key equation here is:

Angular Momentum = Radius x Mass x Velocity

The spinning top demonstrates what we call a ‘gyroscopic effect’ – as the top spins it resists the moment (turning force) generated by gravity acting upon it, as well as the reaction force of the table. 

Challenge

Your task: Use the principles of angular momentum to make a spinning top that will spin for the greatest amount of time.

Optimise your design by using coins to add weight to the spinning top.

How to make your spinning top:

1. Draw three circles on cardboard by tracing around a circular object. Cut them out.
2. Poke a pencil through the middle of one of the cardboard circles. Hold it firmly in place by winding rubber bands around the pencil above and below the cardboard.
3. Secure the cardboard shape where you want it on the pencil (axis of rotation) by winding rubber bands onto the pencil above and below the location. The students should decide where the cardboard shape should be to achieve the optimal performance.
4. With a marker, draw a line at any point on the cardboard spinner top. Have the students spin the spinner. Count the number of rotations the spinner makes within 10 seconds. Write this number down. (The line must be very dark to be able to read it while the shape is spinning.)
5. Now tape six pennies onto the outer rim of one spinner, and six pennies close to the centre of another spinner. Think carefully about where is the best place to add the coins to maximise the spinning top’s performance.
6. Repeat Step 4 with both of these spinners. Has the number of rotations completed within 10 seconds changed? If so why?

(Conservation of angular momentum dictates that the spinner with the pennies at the outer rim should spin slower)

Remember:

Angular Momentum = radius x mass x velocity

Further Reading

Another concept that we might think about here is Precession. Precession is a phenomenon seen when an object spinning about an axis is acted upon  by a moment (turning force) about a second axis. The object is seen to rotate around a third axis. Precession is seen when the spinning top wobbles before toppling over completely.

You can see a demonstration of precession using a bike wheel here , and you can learn more about precession here .

We said that the spinning top demonstrated a gyroscopic effect. What real world impact does this have?

Gyrocompasses were used to navigate on ships and aircraft, gyroscopes are used to ensure the deck of aircraft carriers remain level at all times, and satellites are made to spin as they orbit the Earth to stabilise their flight.

The theory of angular momentum also governs the behaviour of planets orbiting stars and the Moon orbiting the Earth. All of these applications are based on the theory of angular momentum.

Find out more about gyroscopes and build your own boomerang  with the help of Dr Hugh Hunt from the University of Cambridge.

The Museum of Science and Industry, Chicago, explores the theory of angular momentum with instructions of how to build your own roller coaster .

For further information about studying Physics and Engineering at the University of Manchester, you can visit the departments’ webpages .

Bright Knowledge  (part of the Brightside Trust) has key information about studying, and pursuing a career in, Physics and Engineering.