Triple Physics Topic 7 - Moments

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:

The formula is:

moment (newton metre, Nm) = force (newton, N)× perpendicular distance (metre, m)

In physics code:

G = Fd

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.  In the current syllabus, moment is given the code M, which you may prefer.

The units for moment are Newton metre (Nm).

In triangle form:

 Worked Example A spanner 0.30 m long has a force of 20 N applied to it.  What is the moment? Answer Moment = F × d = 20 N × 0.30 m = 6.0 Nm

 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?

 Question 2 How can the force applied be reduced?

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 Show that the seesaw in the picture above is balanced.

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

Moments and Levers

One of the simplest machines is a lever.

There are two forces:

• the effort FE, which is the force we apply to the lever;

• the load FL, which is the force that acts on the object we want to move.

The distance from the effort to the pivot is d, and the distance from the pivot to the load is x.

When we apply the effort, there is a clockwise moment about the pivot:

M = FEd

At the same time there is an opposing anticlockwise moment which is equal in value:

M = FLx

Using the principle of moments, we can write:

FEd = FLx

We can rearrange this to give us:

FL = d

FE    x

What this tells us is that the effort is smaller than the load.  The effort is the same fraction of the load as the distance of the load from the pivot is to the distance from the pivot to the effort.  The ratio d/x is sometimes called the mechanical advantage.  As the load force is much bigger than the effort force, the lever is called a force multiplier.

 Worked example An force of 120 N is applied to a crowbar that is 2 metres long.  The distance from the effort to the pivot is 1.8 m, while the distance from the pivot to the load is 0.2 m What is the load force? What is the mechanical advantage? Answer Use: FL = d = 1.80  = 9.0 FE    x     0.20   FL = 9.0 × 120 = 1080 N   The mechanical advantage is 9.0, which means that the force is multiplied by 9.0.

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?

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?

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?

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.

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

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?

[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 have found 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!]

 Summary Moment is the turning effect of a force Moment = force × perpendicular distance Moments can be clockwise or anticlockwise If anticlockwise and clockwise moments are equal, then the object is balanced. Objects have a centre of mass which is where the mass can be thought of as concentrated. Regular objects have the centre of mass in the middle. A low centre of mass improves the stability of objects.