Moments: Principle of moments.

The idea

The principle of moments states that for an object in rotational equilibrium, the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about that same point. A moment is the turning effect of a force, calculated as force × perpendicular distance from the pivot to the line of action of the force.

For example: A uniform metre rule balanced on a pivot at its centre has a 2.0 N weight 0.30 m to the left and an unknown weight W 0.20 m to the right; taking moments about the pivot gives 2.0 × 0.30 = W × 0.20, so W = 3.0 N. The principle applies to any point, but choosing the pivot often simplifies the calculation because the moment of an unknown reaction force there is zero.

What earns the marks

• The principle of moments applies to an object in rotational equilibrium, meaning it has zero angular acceleration (it is either not turning or rotating at a constant angular velocity).
• The sum of clockwise moments about a point equals the sum of anticlockwise moments about the same point.
• A moment is calculated as force × perpendicular distance from the pivot to the line of action of the force.
• The perpendicular distance is the shortest distance from the pivot to the line of action, measured at right angles to the force.
• The principle can be applied about any point, but choosing the pivot eliminates the moment of the reaction force at that point.
• For equilibrium, both the resultant force and the resultant moment must be zero.

Common mistakes and how to put them right

• Using the distance along the object rather than the perpendicular distance from the pivot to the line of action.

  Put it right: Draw the perpendicular from the pivot to the force line.

• Forgetting to include the weight of the object itself, such as a uniform rule, acting at its centre of mass.

  Put it right: Add its moment about the chosen point.

• Mixing clockwise and anticlockwise moments on the same side of the equation.

  Put it right: Set the sum of clockwise moments equal to the sum of anticlockwise moments.

Exam tips

• Choose the pivot as the point about which to take moments to eliminate unknown forces acting there.
• Draw a clear diagram showing all forces, their lines of action and the perpendicular distances to the pivot.
• Check that all distances are in metres and all forces in newtons before calculating, and state the unit of the answer.