4.1 Turning effects of forces

The centre of gravity is the point through which the resultant weight of an object may be taken to act.

For a uniform symmetric object it is often at the geometric centre; for a non-uniform object it depends on the mass distribution. Use the point to calculate moments.

A uniform metre rule has its weight acting at the 50 cm mark, so its own moment about that point is zero.

The centre of gravity need not lie inside an irregular body, and it is not automatically the centre of the drawing.

The moment (torque) about a pivot is τ=F d⊥, where d⊥ is the shortest perpendicular distance from the pivot to the force’s line of action.

Choose the pivot, resolve the turning sense, and use the perpendicular distance rather than the distance to the point where the force is applied.

A 20 N force acting 0.30 m perpendicularly from a hinge gives a 6.0 N m moment; a force through the hinge gives zero moment.

A large force can have a small moment if its line of action is close to the pivot; distance along the rod is not always d⊥.

A couple consists of two equal, parallel forces acting in opposite directions on different lines. Its resultant force is zero, but it produces a moment.

The turning effect is independent of the chosen pivot. Use the perpendicular separation of the two lines of action and identify the sense of rotation.

Two 15 N forces separated by 0.20 m form a couple with moment 3.0 N m, even though their resultant force is zero.

A pair of equal forces only forms a couple when their lines of action are separated; collinear opposite forces cancel without rotation.

For a couple, moment τ=F s, where F is the magnitude of either force and s is the perpendicular distance between their lines of action.

Use one force magnitude, not the sum of both forces. The couple moment is the same about any pivot because the net force is zero.

Increasing the handle separation from 0.10 m to 0.25 m at 12 N increases the turning moment from 1.2 to 3.0 N m.

Do not use the distance from a pivot to one force when the problem asks for a couple; use the force-line separation.