WJEC Physics for AS Level Student Book 2nd Edition

19 1.1 Basic physics Study point The moment of a force is also called its torque . The symbol lj is sometimes used for moment (or torque). Study point The SI unit of moment is N m . It can also be expressed in kN m , N cm , etc. This is clarified in Fig. 1.1.18. The force F is applied at a distance x from P . But the perpendicular distance from P to the line of action of F is d . So: Moment of F about P = Fd . Looking at Fig. 1.1.18 again we notice that d = x cos θ . \ Moment of F about P = )[ cos θ . We can also write this as ( ) cos θ ) x . If you look at Fig. 1.1.18, you’ll notice that θ is also the angle between the line of action of the force and the vertical grey dotted line. Hence ) cos θ is the component of the force perpendicular to the line joining P and the point of application of F . So this gives an alternative way of calculating the moment of F about P . If we look back at Fig. 1.1.16, we see that the two forces are acting in opposite senses: the small force tends to make the door move clockwise about the hinge; the large force, anticlockwise. We say that the small force has a clockwise moment (CM) and the large force has an anticlockwise moment (ACM). Example Calculate the moment about O of each of the forces in Fig. 1.1.19. Answer (a) The perpendicular distance of the line of action of the 20 N force is 1.5 m from O . \ The clockwise moment of the 20 N force about O = 20 N × 1.5 m = 30 N m . (b) Either : The perpendicular distance of the line of action of the 40 N force is 2.0 m sin 60° from O . \ The ACM of the 40 N force about O = 2.0 m sin 60° × 40 N m = 69.3 N m Or : The perpendicular component of the 40 N force to the 2.0 m displacement is 40 sin 60° . \ The ACM of the 40 N force about O = 40 sin 60° × 2.0 N m = 69.3 N m Now, if those are the only forces acting, the disc in the example will start turning anticlockwise – the anticlockwise moment is larger than the clockwise moment. There is a resultant anticlockwise moment of 69.3 – 30.0 = 39.3 N m . What happens after that is not clear because we don’t know how the forces are applied to the disc; will they stay the same in magnitude, direction and position of application? But it does lead us to an important principle: The principle of moments (PoM) PoM states that, for a body to be in equilibrium, the sum of the anticlockwise moments about any point is equal to the sum of the clockwise moments about the same point. Some people define a positive direction of moment, either clockwise or anticlockwise, and use an alternative, equally valid, statement of the PoM: the PoM states that, for a body to be in equilibrium the resultant moment about any point is zero. (For the time being, we’ll ignore the phrases ‘about any point’ and ‘about the same point’ and come back to them in Section 1.1.7.) Fig. 1.1.19 O 20 N 40 N 1.5 m 2.0 m 60° Knowledge check Identify the moment of each of the forces in Fig. 1.1.15 as CM (clockwise) or ACM. 1.1.9 Fig. 1.1.18 Moment of F about P = Fd line of action of F d F P θ x