The weight of an object can be considered to act at a single point known as its center of gravity.
4.1.2 Moment of a force:
The moment of a force about a point is the product of the force and the perpendicular distance from the point to the line of action of the force.
Moment = force × perpendicular distance = (F x d)
4.1.3 Couples:
A couple consists of a pair of forces with equal magnitude, acting in parallel but opposite directions, and separated by a perpendicular distance.
Couples produce rotation but no net translation.
4.1.4 Torque of a couple:
The torque (also known as the moment of a couple) is the product of one of the forces and the perpendicular distance between the forces.
Torque = force × perpendicular distance
4.2 Equilibrium of forces:
4.2.1 Principle of moments:
The principle of moments states that for a body in equilibrium, the sum of the clockwise moments about any point is equal to the sum of the anticlockwise moments about the same point.
4.2.2 Equilibrium conditions:
When there is no resultant force and no resultant torque acting on a system, it is in equilibrium.
4.2.3 Vector triangle representation:
Coplanar forces in equilibrium can be represented by a closed vector triangle, where the lengths of the vectors represent the magnitudes of the forces and the direction of the vectors represents the direction of the forces.
4.3 Density and pressure:
4.3.1 Density:
Density is the mass per unit volume of a substance.
Density = mass/volume = m/V
4.3.2 Pressure:
Pressure is the force per unit area exerted on a surface.
Pressure = force/area, P = F/A
4.3.3 Hydrostatic pressure:
Hydrostatic pressure is the pressure exerted by a fluid at rest.
The equation for hydrostatic pressure is ∆p = ρg∆h, where ∆p is the change in pressure, ρ is the density of the fluid, g is the acceleration due to gravity, and ∆h is the change in height.
4.3.4 Upthrust and Archimedes' principle:
The upthrust acting on an object immersed in a fluid is equal to the weight of the fluid displaced by the object.
The upthrust can be calculated using the equation F = ρgV, where F is the upthrust force, ρ is the density of the fluid, g is the acceleration due to gravity, and V is the volume of the fluid displaced by the object.