Question

P, Q and R are the three forces, each of magnitude 6 N acting in the plane of paper as shown in Fig. The point O lies in the same plane.

1. Which force has the least moment about O?
2. Which force has the greatest moment about O?
3. Name the forces producing (a) clockwise, (b) anticlockwise moments.
4. What is the resultant torque about the point O?

Answer 1

Since all three forces have the same magnitude, the moment depends on the perpendicular distance from O to the line of action of the force.

Moment of a force = Force × perpendicular distance

(i) Force R has the least moment about O.

τR​ = 6 × 0.6 

= 3.6 N m

(ii) Force P has the greatest moment about O.

τP​ = 6 × 0.9

= 5.4 N m

Force Q produces:

τQ​ = 6 × 0.8

= 4.8 N m

The moment is calculated using τ = F × d, where ddd is the perpendicular distance from O to the line of action of the force.

(iii) (a) P and Q produce clockwise moments.

(iii) (b) R produces an anticlockwise moment.

(iv) Resultant torque about O:

Clockwise torque = 5.4 + 4.8

= 10.2 N m

Anticlockwise torque = 3.6 N m

Resultant torque = 10.2 − 3.6

= 6.6 N m 

Therefore, the resultant torque about point O is 6.6 N m clockwise.