Define the moment of a force and state its unit.
State the principle of moments.
Define a couple and the torque of a couple.
A force of 25 N acts at a perpendicular distance of 0.30 m from a pivot. Find the moment.
A force of 40 N acts at a perpendicular distance of 0.15 m from a hinge. Find the moment.
A seesaw balances with a 250 N child 1.2 m from the pivot. How far from the pivot on the other side must a 300 N child sit to balance it?
A uniform metre rule is pivoted at its centre (the 50 cm mark). A 2.0 N weight hangs at the 20 cm mark. Where on the other side must a 3.0 N weight hang to balance the rule? Give the mark on the rule.
Two parallel forces of 6.0 N act in opposite directions, 0.40 m apart, forming a couple. Find the torque of the couple.
A force of 15 N is applied at the end of a 0.20 m spanner, at 50 degrees to the spanner. Find the moment about the nut.
Explain why the perpendicular distance, rather than the distance along the arm, must be used when a force is applied at an angle.
Total: 24 marks. Original work by the TheLucidSTEM team. Written in the style of the papers; no past paper question is reproduced.
Answer key · full worked solutionsclick to reveal
the moment of a force about a point is the force multiplied by the perpendicular distance from the point to the line of action of the force; unit N m.
for a body in equilibrium, the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about that point.
a couple is a pair of equal, opposite, parallel forces whose lines of action do not coincide. The torque of a couple is one of the forces multiplied by the perpendicular distance between them; unit N m.
moment = 25 × 0.30 = 7.5 N m.
moment = 40 × 0.15 = 6.0 N m.
250 × 1.2 = 300 × d, so 300 = 300d and d = 1.0 m from the pivot.
the 2.0 N weight is 0.30 m from the pivot (50 cm − 20 cm). 2.0 × 0.30 = 3.0 × d, so 0.60 = 3.0d and d = 0.20 m. The 3.0 N weight hangs 0.20 m from the centre on the other side, at the 70 cm mark.
torque = one force × perpendicular distance = 6.0 × 0.40 = 2.4 N m.
moment = 15 × 0.20 × sin 50° = 15 × 0.20 × 0.766 = 2.3 N m.
only the component of the force perpendicular to the arm produces a turning effect. Using the perpendicular distance (the distance along the arm multiplied by the sine of the angle) accounts for this; the full distance along the arm would overstate the moment.