3.2.3 Equilibrium

The moment of a force is the turning effect of a force about an axis or point. It equates to the product of force and the perpendicular distance of the line of action of the force from the axis or point of rotation:

moment = F x

Units: N m

When a body is in equilibrium the net force acting on it is zero and its net moment is zero. The principle of moments can be used to solve problems where an object is in rotational equilibrium. The principle of moments states that for a body in rotational equilibrium the sum of the anticlockwise moments abut any point is equal to the sum of the clockwise moments about the same point.

A pair of equal but opposite forces that are parallel and act on different lines is known as a couple. The moment of a couple is known as a torque. The torque of a couple is the product of one of the forces and the perpendicular separation between the forces:

torque of a couple = Fd

The centre of mass of an object is a point through which any externally applied force produces straight line motion with no rotation. The centre of gravity of an object is an imaginary point were the entire weight of an object appears to act. A freely suspended object will come to rest with its centre of gravity vertically below the point of suspension. We can use a plumb-line to experiment about the centre of gravity (for 2-D objects).

When an object is in equilibrium there is no resultant force acting on it. We can demonstrate the forces in a free-body diagram using a triangle of forces:

• arrows are drawn to represent each of the three forces end to end (ie the end of one arrow is the beginning of the next)
• the triangle is closed if the object is in equilibrium. this is because the et force is zero and so the object is in equilibrium.