P3aL1 Just a Moment

Key Words

Anticlockwise moment - a moment that goes anticlockwise (really?)

Axis of rotation - the pivot around which a force turns

Centre of mass - an imaginary point around which all the mass is thought to act.

Clockwise moment - a moment that goes clockwise (really?)

Force - a push, pull, or twist.

Moment - the turning effect of a force.

Turning effect - how a force makes an object turn.

Grade E

A moment is the turning effect of a force around a pivot (or axis of rotation).

The turning moment is worked out using the equation:

moment (Nm) = force (N) × perpendicular distance from the line of action of the force to the pivot (m)

This particular force will make a clockwise moment.  If the force were the other side of the pivot, the moment would be anticlockwise.

If we have two forces, F and F' (pronounced "F-dashed" or "F-prime") acting on the lever, and it stays horizontal, we say that:

the anticlockwise moment = the clockwise moment

The rod is balanced.

By the Principle of Moments:

F × x = F' × y

Grade C

The centre of mass is an imaginary point where all the mass is concentrated.  This idea of point masses makes mechanics problems a lot simpler.  In regular shaped (uniform) objects like a ball, or a ruler, the centre of mass is right in the middle of the object.

For symmetrical objects, the centre of mass is always on a line of symmetry.  If there is more than one line of symmetry, the centre of mass is where lines meet.

In some objects the centre of mass is not even in the body of the object, for example in this ring.

At this level it does not matter at all where the centre of mass is; all objects can be thought of as point masses.  The lines of action of any forces act through the centre of mass.

In objects that are not uniform, like a cone, the centre of mass is near the bottom. 

A simple experiment involves balancing a ruler from a pivot that is not exactly in the middle.

The ruler is a regular object, so its centre of mass is exactly in the middle, at the 50 cm mark.  We can work out what the force is, using the principle of moments.  Notice that we will use 0.20 m rather than 20 cm so that our units are consistent with the units of Nm.

anticlockwise moment = clockwise moment

F × 0.20 m = 2 N × 0.30 m

F = 3 N

Grade A

Moments can be used to perform this little trick:

If you tap the pen firmly, the paper does not move up into the air, as you might expect.  It moves horizontally.

The angle between the line of action of the force from the pen and the paper does not remain at 90^o, but changes.

A heavier flat object like a place mat does not move horizontally; one side flips into the air and falls back.