Topic 4 – Moments and Equilibrium

Turning Effects of a Force

If we have hinged or pivoted body, any force applied changes the rotation of that body about the pivot. The turning effect is called a moment.

The equation is:

Moment = force × perpendicular distance

In Physics code:

                                                            G = Fs

This strange looking symbol, G, is “gamma”, a Greek capital letter ‘G’.  Units are newton metres (Nm).

Moments have a direction.  As they are turning effects, we can talk of clockwise and anti-clockwise moments. By convention, clockwise is positive.

Consider a trap door held by a piece of string, BC.  P and Q are forces.  The trap door is hinged about point O.

The perpendicular distance of the line of action of force Q is the length of the line OC.

Moment of P about O = P × OA

Moment of Q about O = Q × OC

Note that the Moment of Q about O is [Q ×OC]. This is because OC is the perpendicular distance of the force Q from the hinge O.

If the trap door remains in equilibrium:

Anticlockwise moment (Q × OC) = clockwise moment (P ×OA)

This is the Principle of Moments.

Since OC = OB sin q we can say that  Q × (OB sin q) =  P × OA

Centre of Gravity

We treat objects as point masses referring to a single point called the centre of gravity.

In regular object like a cube or a sphere, the centre of gravity is in the middle.  In some objects the centre of mass is outside the object.

The centre of gravity is the point through which the entire weight is said to act.  Objects with a very low centre of gravity tend to be very stable.  Some objects are so stable that they never fall over.  Objects with a high centre of gravity are unstable.

Balancing

Many questions involve the balancing of see-saw around pivots.  Let us look at some situations:

This is the simplest case.  The pivot is in the middle of a uniform bar.  It means that the object is totally regular and the centre of mass is in the middle.  Therefore we can ignore the mass of the bar.  If the bar is balanced, we can say that:

anticlockwise moments = clockwise moments

Ax = By

Let is look at a case where we move the pivot P.

In this case, the line of action of the weight, W, is z metres from the pivot P.  Applying the principle of moments we can say:

Ax = By + Wz

As an extension exercise click HERE to see how to do problems involving bridges (these will NOT be set in the AS Exam)

Couples

If two forces act about a hinge in opposite directions, there is an obvious turning effect called a couple. The resulting linear force from a couple is zero.

The couple is given by the simple formula:

G = 2 Fs

This strange looking symbol, G, is “gamma”, a Greek capital letter ‘G’.  Couples are measured in Newton metres (Nm)

The turning effect is often called the torque.  It is a common measurement made on motors and engines, alongside the power.  Racing engines may be quite powerful but not have a large amount of torque.  This is why it would not make sense for a racing car to be hitched to a caravan, any more so than trying to win a Formula 1 race in a 4 x 4.