Moments and pressure

Revision notes

A force can produce a turning effect about a pivot. The moment of a force is moment = force × perpendicular distance from the pivot to the line of action of the force, M = Fd. The perpendicular distance matters: measuring to the wrong point or along a sloping force gives the wrong moment. For an object in rotational equilibrium, the total clockwise moment about a chosen pivot equals the total anticlockwise moment. Levers use this idea to trade force for distance.

Pressure describes force spread over area, p = \(\dfrac{F}{A}\). For the same normal force, a smaller contact area gives a larger pressure. This explains why sharp blades cut more readily and why wide tyres or tracks can reduce pressure on soft ground. In fluids, pressure acts normal to surfaces. Liquid pressure increases with depth and with liquid density: the pressure difference caused by a liquid column is p = hρg.

Because pressure usually increases with depth, a submerged object can experience a greater upward force on its lower surface than the downward force on its upper surface. The resulting upward force is upthrust. An object floats when forces balance; in a stable floating state the upthrust equals the object's weight.

Moments and turning effects

A force can produce a turning effect about a pivot. The moment is M = Fd, where d is the perpendicular distance from the pivot to the force's line of action. The perpendicular distance matters: increasing lever length can increase turning effect without changing force.

For an object in rotational equilibrium, total clockwise moment equals total anticlockwise moment. This principle is used in balances, seesaws and lever systems. In calculations, choose one pivot, identify each perpendicular distance and keep units consistent.

Levers and mechanical advantage

Levers allow a smaller force to produce a larger turning effect by increasing distance from the pivot. This does not create energy. In an ideal system, a smaller input force acts through a larger distance while the load moves through a smaller distance. Real systems also lose energy through friction and deformation.

Pressure on surfaces

Pressure is force per unit area, p = \(\dfrac{F}{A}\). For the same force, a smaller contact area produces greater pressure. This explains why sharp blades cut effectively and why wide tyres, snowshoes or tracks can reduce pressure on soft ground.

Area must be in square metres for pressure in pascals. Be especially careful converting cm² to m²: the conversion factor is squared.

Pressure in fluids and upthrust

Fluid pressure acts in all directions and increases with depth because deeper points support a greater weight of fluid above. The pressure difference due to a column of liquid is p = hρg, so it also increases with the density of the liquid. Atmospheric pressure decreases with height because there is less air above. A pressure difference between the lower and upper surfaces of an immersed object can produce an upward resultant force called upthrust.

A floating object is not free from gravity. Its weight downward is balanced by upthrust upward. If weight exceeds upthrust it accelerates downward; if upthrust exceeds weight it accelerates upward.

Exam technique

For moment questions, draw the pivot and perpendicular distances before calculating. For pressure questions, separate force from area. For floating questions, describe a force balance rather than saying that water 'holds the object up' without naming upthrust and weight.

Levers and gears (separate physics)

A lever is a simple machine that uses moments. A small force applied far from the pivot produces a large moment, which can exert a large force close to the pivot; this is how a crowbar or wheelbarrow works.

Gears transmit the rotational effect of a force. When a small gear drives a larger gear, the larger gear turns more slowly but with a larger moment. When a large gear drives a smaller gear, the smaller gear turns faster with a smaller moment.