newton's laws of motion back to teaching back to the course first page of this section previous page next page last page of this section help on navigating these pages

You will all be familiar with Newton's laws of motion, so we will just summarize them here, using the symbols F for force (which is a vector quantity), v for velocity (also a vector quantity) and m for mass (which is a scalar).

law I      Unless a resultant force acts on a body, its velocity will not change.

i.e. if F = 0, v = 0

This gives us an intuitive meaning of force: a resultant force is that agent which changes the velocity (and momentum) of a body. Law I is a special case of law II.

law II    The rate of change of momentum of a body is proportional to the resultant force that acts on it.

i.e.      F d(mv)/dt

or        F = k d(mv)/dt

Hence  F = km dv/dt + kv dm/dt

              = km dv/dt   (since dm/dt = 0 in most problems in classical mechanics)

              = kma

We then choose k=1, and in so doing we also define our unit for force.

F[N] = m[kg]a[ms-2]

1 newton (N) is that force which accelerates a mass of 1 kg at 1 ms-2.
F = ma is one form of Newton's second law.

law III   If body A exerts a force F on body B, then body B exerts a force F on body A of the same size and along the same line, but in the opposite direction.

i.e. FAB = - FBA

Law III refers to a pair of forces which must always act on two different bodies. These two forces have the same size at every instant of time.

©Vik Dhillon, 30th September 2009