1. Turning Effects of Forces
Turning effects
Moments, couples and centre of gravity
The centre of gravity of an object is the single point at which its whole weight may be taken to act. For a uniform rod it is at the midpoint.
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.
A couple is a pair of forces equal in magnitude, opposite in direction and not acting along the same line. Its resultant force is zero, so it produces rotation only. The torque of a couple = one of the forces × the perpendicular distance between their lines of action.
Turning effects
moment = F × d⊥ torque of a couple = F × d (d = perpendicular separation of the forces)
Worked Example
A force of 50 N is applied to the end of a spanner 0.30 m from the nut, at 60° to the spanner. Find the moment about the nut.
Practice Question
A driver turns a steering wheel of diameter 0.40 m by pushing with 15 N tangentially at opposite ends of a diameter. Find the torque.
2. Equilibrium of Forces
Equilibrium
Principle of moments and vector triangles
An object is in equilibrium when there is no resultant force and no resultant torque on it: it neither accelerates nor starts to rotate.
Principle of moments: for an object in equilibrium, the sum of the clockwise moments about any point equals the sum of the anticlockwise moments about the same point. Take moments about the point where an unknown force acts to remove it from the equation.
When three coplanar forces keep an object in equilibrium, drawing them head to tail gives a closed triangle. You can solve it by scale drawing or trigonometry, or by resolving horizontally and vertically.
Worked Example
A uniform plank 4.0 m long and of weight 200 N rests on supports at each end. A person of weight 600 N stands 1.0 m from the left end. Find the support forces.
Worked Example
A lamp of weight 20 N hangs from a cable that makes 30° with the vertical; the lamp is pulled aside by a horizontal string. Find the tension in the cable and in the string.
Practice Question
A uniform metre rule of weight 1.2 N is pivoted at its 30 cm mark. Where must a 2.0 N weight be hung to balance it?
3. Density and Pressure