Quick questions on Forces, equilibrium and moments explained: H2 Physics Newtonian Mechanics

In mechanics problems you meet weight (gravity acting at the centre of gravity), the normal contact force (perpendicular to a surface), friction (along a surface, opposing relative motion), tension (along a string or rod) and the upthrust on a body in a fluid. Identifying every force is the first step in any equilibrium problem.

The moment (or torque) of a force about a point measures its turning effect:

A couple is a pair of equal, opposite, parallel forces whose lines of action do not coincide. A couple produces a turning effect with no resultant force. Its torque is:

An extended rigid body is in equilibrium when both conditions hold:

Taking moments about an unknown force removes it from the equation; failing to do so makes the algebra harder.

State the two conditions for the equilibrium of an extended body. [2 marks]

A $30\ \text{N}$ force acts at the end of a spanner $0.25\ \text{m}$ long, perpendicular to it. Find the moment about the nut. [1 mark]

A uniform bar of weight $40\ \text{N}$ and length $2.0\ \text{m}$ is pivoted at its centre. A $10\ \text{N}$ weight hangs $0.80\ \text{m}$ to the left of the pivot. Where must a $16\ \text{N}$ weight hang to balance it?