# Forces - Centre of Mass 01

This GCSE Physics quiz on forces looks at centre of mass. You may have seen video clips of high wire (tightrope) walkers crossing between tall buildings. They will usually have a long pole that they hold out horizontally. This actually changes their centre of mass, placing it below the wire and making them much less likely to fall. The same idea can be used for the party trick of balancing a cork on a needle using two forks stuck into the cork on opposite sides.

Balancing an object is all about the centre of mass. Objects with a wide base and low centre of mass are more stable than those with a narrow base and high centre of mass. When you are on a bus, train, tram etc and have to stand up, spreading your legs a little wider than normal helps to make you more stable.

Formula one racing cars can go round corners much faster than a family saloon car because they have a wide base and a very low centre of gravity.

The term 'centre of mass' represents a unique point in an object or system through which the entire mass of the object acts. Assuming the mass of an object acts at a point allows us to calculate how objects will respond to different forces. It is sometimes referred to as the centre of gravity. Finding the centre of mass for a regularly shaped object with a uniform density is easy, it can be done by drawing.

If you have an irregular shaped or non-symmetrical object, you need to do that by experiment. You will need to drill a hole into the object and hang it up. Then, you hang a plumb line (that's a piece of string with a mass attached to the end) from the same support point and carefully draw a straight line down the object. Next, you repeat the experiment but by drilling a hole on a different place in the object. Where the two lines cross is the centre of mass. You can repeat it even more times to improve the accuracy.

But why does that work? When an object is suspended from a point around which it can freely turn, the centre of mass will be directly below the suspension point. This is illustrated by a pendulum. If a pendulum is pushed or pulled sideways, the centre of mass is no longer directly beneath the suspension point. The pendulum is out of balance and therefore 'falls' back towards the point at which it is balanced. It will then swing backwards and forwards, until air resistance and friction bring it to a halt, with the centre of mass directly below the suspension point. The point of balance is actually the point of the lowest gravitational potential energy and represents the greatest stability. Interestingly, the time taken by a pendulum to make one swing does not depend on the mass of the pendulum, but its length. For the GCSE, you need to know the formula that relates the time taken for a pendulum to complete one full swing (the time period) is related to the number of swings it makes in one second (the frequency).

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1. A freely suspended object will come to rest with its centre of mass directly below which point?
This is the position of lowest gravitational potential energy and therefore the most stable arrangement
2. What does the time period depend on?
A longer length of pendulum will increase the time period of the oscillation. Conversely, a shorter pendulum will have a shorter period of oscillation
3. How can you locate the centre of mass of an irregular object?
Where the two lines made by the plumb line cross is the centre of mass
4. What is the time period if the frequency is 100 Hz?
This is a simple case of substituting the figures into the formula
5. What is the formula for the period of oscillation for a simple pendulum?
The time period for a simple pendulum is related to the frequency of the pendulum. Knowing the time period or the frequency will allow you to work out the other
6. A simple pendulum oscillates 50 times per second. What is the frequency of the pendulum?
You don't even need to use the equation for this, all you need to know is the definition of hertz
7. Where is the centre of mass located on a rectangle of length 5 cm and width 3 cm if the mass is distributed evenly throughout the object?
For an object such as this, the centre of mass is at the centre
8. What is the frequency of a simple pendulum if the time period is ten seconds?
One hertz = one complete swing of the pendulum in one second so in this case, just one tenth of a complete swing occurs in one second
9. What is centre of mass?
For large bodies like the Sun and planets, their gravitational field appears to originate from their centre of mass
10. Where is the centre of mass located in a regularly shaped object?
For a non-symmetrical object, it is more difficult to find

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