Mass, Weight and Force Basics

Mass — a measure of the amount of matter in a body, and of its resistance to being accelerated. A scalar, measured in kilograms, and the same everywhere in the universe.

Weight — the gravitational force acting on a mass. A vector, measured in newtons, and it changes with location.

W = mg

Gravitational field strength (g) — the force per unit mass acting on a body in a gravitational field, measured in N kg⁻¹. Near the Earth's surface it is about 9.81 N kg⁻¹.

Example: the same quantity has two names and two units. As a field strength it is 9.81 N kg⁻¹; as the acceleration of a freely falling object it is 9.81 m s⁻². These are dimensionally identical — N kg⁻¹ is kg m s⁻² ÷ kg — and it is worth checking that for yourself once.

Mass and weight are not interchangeable — an astronaut with a mass of 80 kg has a weight of about 785 N on Earth and about 130 N on the Moon, where g is roughly 1.6 N kg⁻¹. Their mass has not changed. Bathroom scales measure force and are calibrated to display mass assuming Earth's g, which is why they would read wrong on the Moon.

Centre of mass — the single point at which the whole weight of a body can be taken to act. For a uniform, symmetrical object it lies at the geometric centre.

The forces you will meet

Weight — always acts vertically downwards, from the centre of mass.

Normal contact force — acts perpendicular to a surface, pushing the object away from it. It is not always equal to the weight: on a slope it equals only the perpendicular component.

Friction — opposes relative motion between surfaces, acting along the surface.

Drag — opposes motion through a fluid, and increases with speed.

Tension — acts along a rope or spring, pulling inwards at both ends.

Upthrust — the upward force from a fluid on a body immersed in it.