 The frequency of a simple pendulum if the time period is ten seconds is 0.1Hz.

# Forces - Centre of Mass

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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 center 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 center of mass are more stable than those with a narrow base and high center of mass. When you are on a bus, train, trolley car etc and have to stand up, spreading your legs a little wider than normal helps to make you more stable.

Formula one race cars can go round corners much faster than a family sedan because they have a wide base and a very low center 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 center of gravity. Finding the center 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 center 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 center of mass will be directly below the suspension point. This is illustrated by a pendulum. If a pendulum is pushed or pulled sideways, the center 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 center 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. In senior high school, 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).

1.
How can you locate the center of mass of an irregular object?
Suspend the object from two locations and drop a plumb line from the suspension points
Suspend the object from one location and drop a plumb line from the suspension point
Measure to the center of the object
None of the above
Where the two lines made by the plumb line cross is the center of mass
2.
What is the time period if the frequency is 100 Hz?
1 s
0.1 s
0.01 s
0.001 s
This is a simple case of substituting the figures into the formula
3.
A freely suspended object will come to rest with its center of mass directly below which point?
Point of recession
Point of suspension
The center of mass doesn't lie directly below any point
None of the above
This is the position of lowest gravitational potential energy and therefore the most stable arrangement
4.
What does the time period depend on?
Force with which the pendulum is released
Width of string used in the pendulum
Length of the pendulum
All pendulums have the same time period
A longer length of pendulum will increase the time period of the oscillation. Conversely, a shorter pendulum will have a shorter period of oscillation
5.
Where is the center of mass located on a rectangle of length 5 cm and width 3 cm if the mass is distributed evenly throughout the object?
(1.5,2.5)
(3,5)
(2.5,1.5)
(5,3)
For an object such as this, the center of mass is at the center
6.
Where is the center of mass located in a regularly shaped object?
Along an axis of symmetry
Always in the center of the object
Always 2cm to the left of the center
Always 2cm to the right of the center
For a non-symmetrical object, it is more difficult to find
7.
What is center of mass?
It is the point at which the mass of an object may be thought to be concentrated
The point at which an object has no mass
A number of points across an object which measure the same mass
None of the above
For large bodies like the Sun and planets, their gravitational field appears to originate from their center of mass
8.
What is the formula for the period of oscillation for a simple pendulum?
T = 2f
T = 3f
T = 4f
T = 1f
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
9.
A simple pendulum oscillates 50 times per second. What is the frequency of the pendulum?
25 Hz
50 Hz
75 Hz
100 Hz
You don't even need to use the equation for this, all you need to know is the definition of hertz
10.
What is the frequency of a simple pendulum if the time period is ten seconds?
0.01 Hz
0.1 Hz
1 Hz
10 Hz
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
Author:  Martin Moore