Moments calculator: M = Fd with working

Example: a 20 N force acts 0.5 m from a pivot. $M = 20 \times 0.5 = 10$ N m.

When an object is balanced, the total clockwise moment equals the total anticlockwise moment about the pivot (the principle of moments).

Example: on a see-saw, a 300 N child sits 2 m from the pivot. Where must a 200 N child sit to balance? Anticlockwise moment $= 300 \times 2 = 600$ N m. So $200 \times d = 600$, giving $d = 3$ m. In the calculator: moment 600, force 200, find the distance.

A lever lets a small force exert a large one: pushing far from the pivot creates a big moment, which acts on a load close to the pivot. Spanners, crowbars and wheelbarrows all work this way. Gears transmit the rotational effect of a force: a small gear driving a bigger one turns it more slowly but with a bigger moment.

The distance must be at right angles to the force. If a force pulls at an angle, the perpendicular distance from the pivot to its line is shorter than the length of the lever, so the moment is smaller. Exam diagrams usually give the perpendicular distance directly.

• Measuring the distance from the end of the object instead of the pivot.
• Leaving distances in cm: 50 cm is 0.5 m.
• Using mass instead of weight: multiply kg by 9.8 to get newtons.

Practise with our moments questions.

• Choose the pivot, then list each force with its perpendicular distance.
• Label each moment clockwise or anticlockwise before balancing.
• Distances in cm can be kept in cm on both sides when balancing (they cancel), but give moments in N m when asked for a moment.
• For a uniform beam, its weight acts at its centre.