If an object is balanced, the total clockwise moment about a pivot equals…

The idea

Balanced means the beam is not turning, requiring the sum of every clockwise turning effect about the pivot to match the sum of every anticlockwise one. Each moment is worked out separately as force multiplied by perpendicular distance and then added to its own side. On a number balance, a 2-unit weight hung at position 3 on the right gives a clockwise moment of 6 units. To balance this, 6 units of anticlockwise moment must be restored on the left, for example by hanging one 1-unit weight at position 6, or one 2-unit weight at position 3. If the two totals are not equal there is a resultant moment and the beam turns the way the larger one points. The pivot supplies whatever upward force is needed to balance the downward forces.

What earns the marks

• Stating the total clockwise moment equals the total anticlockwise moment.
• Each moment worked out as force × perpendicular distance from the pivot.
• Summing all the moments on each side before comparing them.
• Stating the direction of the resultant moment where the totals differ.

Common mistakes and how to put them right

• Adding forces instead of moments when more than one weight hangs on the same side.

• Measuring distances from the end of the beam rather than from the pivot.

• Assuming a balanced beam needs equal weights, ignoring their distances from the pivot.

• Leaving out the moment of a second load on one side.

Exam tips

• Tabulate the force and the distance for every load before writing the balance equation.
• State which way the beam turns when the moments are unequal; it is usually a mark on its own.