Topic 1

How do forces have a turning effect?

Moments

The turning effect of a force is called a moment.

A moment is NOT a period of time.  Nor is it the same as momentum.

Moment is the product (two numbers multiplied together) between the force and the perpendicular distance from the force and the pivot.  To show what this means, look at the picture:

There is a formula you need to learn:

The strange looking symbol G (looks a bit like a gallows) is "Gamma", a Greek capital letter 'G'.  It's the physics code for moment.

The units for moment are Newton metre (Nm).

In triangle form:

Worked Example

Question 1  A wheel nut is tightened to a moment of 100 Nm.  A motorist has to undo the nut with a wheel wrench which is 0.40 m long.  What force must he apply?  ANSWER

Question 2  How can the force applied be reduced?  ANSWER

Balancing Moments

Moments have two possible directions, clockwise or anti-clockwise.

• If the clockwise moment is bigger than the anticlockwise moment, then the object will turn clockwise.

• If the anticlockwise moment is bigger than the clockwise moment, then the object will turn anticlockwise.

• If the clockwise moment is equal to the clockwise moment, then the object will stay where it is.

This leads to an important rule in Physics, the Principle of Moments:

If the clockwise moment = anticlockwise moment, the system is in equilibrium

This means that the system is balanced:

Question 3.  Can you show that the seesaw in the picture above is balanced?  ANSWER

Question 4.  The seesaw above is balanced.  What is the force F?  ANSWER

Centre of Mass

In Physics we find it a lot easier to think of objects as point masses.  All objects have a point at which they balance, called the centre of mass.  We think of all the mass as being concentrated at the centre of mass.

The centre of mass is the point at which the weight of the object is said to act.  The green arrow is the line of action of the force from the centre of mass.  Force due to gravity on a mass is the weight.

Note that it is called the centre of mass not centre of weight.  This is because if the object were in space, it would still have a centre of mass, even though it were weightless.  Sometimes the centre of mass is called the centre of gravity.

Question 5  What happens if the line of action of the force is to the right of the pivot?  ANSWER

For any regular object, e.g. box, a cylinder, etc., the centre of mass is in the very centre of the object.

If we allow an object to dangle freely from a single point, we find that the centre of mass is on a line vertically underneath the point from which the object is hung.

We can trace the line by hanging a plumb line (heavy object on a string) which always hangs vertically.

Now if we turn the rectangle so that it hangs off one of the holes in the corner, we can use the plumb line to trace a second line like this:

We could do the same hanging the rectangle from the opposite corner.

Question 6.  Where is the centre of mass?  ANSWER

Centre of Mass and Stability

Stability is the extent to which an object resists toppling over.  Stable objects do not topple over easily.  When designing vehicles, engineers try to design so that the centre of mass is as low as possible.  This makes vehicles less likely to turn over when going round corners.

Let's look at this more closely using a double-decker bus:

You can see the line of action from the centre of mass.  It is in the middle of the track (distance between the wheels) of the bus.

Now suppose the bus goes fast round a corner and tilts over.

There is a moment between the pivot and line of action of the weight

Question 7  What direction is this moment.  What will the effect be on the bus?  ANSWER

Now suppose the bus goes even faster round a sharp bend:

Here you can just see that the line of action of the weight is outside the track.

Question 8  Which way is the moment now?  What will happen to the bus?  ANSWER

You can see from the diagram that the bus has to tilt to a ludicrous angle before it tips over.  Buses are designed to:

• have a low centre of mass;

• have a wide track.

Question 9  What features would be seen on a vehicle that is quite likely to tip over when it tilts?  ANSWER

[Note for Scottish readers: You may recognise the vehicle as an Edinburgh bus.  I must point out that Edinburgh buses are among the best in the entire UK, and I find bus travel in Edinburgh a very pleasant experience.  I have nothing but praise for the Edinburgh bus service, even though I normally hate bus travel.  The drivers are highly professional and would not drive their vehicles as shown!]

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