|newton's laws of motion|
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.
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)
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.
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
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.