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1 of 26 © Boardworks Ltd 2009 2 of 26 © Boardworks Ltd 2009 Introduction to turning forces Forces can make things accelerate. They can also make things rotate. What’s wrong with these pictures? too short! too short! wrong place! We know instinctively that we need to apply a force at a large distance from the pivot for it to be effective. 3 of 26 © Boardworks Ltd 2009 Moments and torque A moment is the turning effect of a force. It can also be called a torque. Torque is given the symbol t (the Greek letter tau). Its units are newton metres (Nm). pivot F d F – the force applied in newtons (N). d – the perpendicular distance (in m) between the pivot and the line of action of the force. t=F×d 4 of 26 © Boardworks Ltd 2009 Moments for non-perpendicular distance 5 of 26 © Boardworks Ltd 2009 Couples and torques A couple is a pair of forces acting on a body that are of equal magnitude and opposite direction, acting parallel to one another, but not along the same line. Forces acting in this way produce a turning force or moment. The torque of a couple is the rotation force or moment produced. F d 6 of 26 F The forces on this beam are a couple, producing a moment or torque, which will cause the beam to rotate. © Boardworks Ltd 2009 The torque of a couple There is a formula specifically for finding the torque of a couple. A point P is chosen arbitrarily. Take moments about P. F P d–x x d total moment = Fx + F(d – x) F = Fx + Fd – Fx = Fd perpendicular distance torque of a couple = force × between lines of action of the forces 7 of 26 © Boardworks Ltd 2009 Moments: testing 8 of 26 © Boardworks Ltd 2009 9 of 26 © Boardworks Ltd 2009 Centres of mass and gravity The centre of gravity of an object is a point where the entire weight of the object seems to act. The centre of mass of an object is a point where the entire mass of the object seems to be concentrated. In a uniform gravitational field the centre of mass is in the same place as the centre of gravity. An alternative definition is that the centre of mass or centre of gravity of an object is the point through which a single force has no turning effect on the body. 10 of 26 © Boardworks Ltd 2009 Finding the centre of gravity 11 of 26 © Boardworks Ltd 2009 Centre of gravity: testing 12 of 26 © Boardworks Ltd 2009 13 of 26 © Boardworks Ltd 2009 Equilibrium A body persists in equilibrium if no net force or moment acts on it. Forces and moments are balanced. Newton’s first law states that a body persists in its state of rest or of uniform motion unless acted upon by an external unbalanced force. Bodies in equilibrium are therefore bodies that are at rest or moving at constant velocity (uniform motion). F1 F2 F2 F1 equilibrium 14 of 26 © Boardworks Ltd 2009 Balanced moments If the total clockwise moment on an object is balanced by the total anticlockwise moment, then the object will not rotate. Provided that there are no other unbalanced forces on it, the object will be in equilibrium, like the beam below: 4m 3N 2m 6N total anticlockwise moments = total clockwise moments 3×4=6×2 12 Nm = 12 Nm 15 of 26 © Boardworks Ltd 2009 The principle of moments The principle of moments states that (for a body in equilibrium): total clockwise moments = total anticlockwise moments This principle can be used in calculations: 5m What is d? d 4 × 5 = 6d 4N 6N 20 = 6d d = 20 / 6 d = 3.3 m 16 of 26 © Boardworks Ltd 2009 Can you make the beam balance? 17 of 26 © Boardworks Ltd 2009 Balancing moments calculations 18 of 26 © Boardworks Ltd 2009 Human forearm The principle of moments can be used to find out the force, F, that the biceps need to apply to the forearm in order to carry a certain weight. When the weight is held static, the system is in equilibrium. Taking moments about the elbow joint: 4F = (16 × 20) + (35 × 60) 4F = 2420 weight of arm = 20 N 60 N 4 cm F schematic diagram 16 cm 20 N 35 cm 60 N F = 605 N 19 of 26 © Boardworks Ltd 2009 Centre of gravity and equilibrium 20 of 26 © Boardworks Ltd 2009 Finding the weight of a metre rule The uniform metre rule shown is in equilibrium, with its centre of gravity marked by the arrow ‘weight’. Find the weight of the metre rule. 0.2 m 3N 0.3 m 0.5 m W total anticlockwise moments = total clockwise moments 3 × 0.2 = weight × 0.3 weight = 0.6 / 0.3 weight = 2 N 21 of 26 © Boardworks Ltd 2009 Equilibrium: testing 22 of 26 © Boardworks Ltd 2009 23 of 26 © Boardworks Ltd 2009 Glossary 24 of 26 © Boardworks Ltd 2009 What’s the keyword? 25 of 26 © Boardworks Ltd 2009 Multiple-choice quiz 26 of 26 © Boardworks Ltd 2009