Newton’s laws, momentum and impulse

Most of the mechanics taught in first year university courses will be the same for this topic, so there shouldn’t be too much you haven’t seen before here! There are some links between equations that you may not be aware of though, so read on…

Newton’s laws:

  1. An object remains at rest or in uniform acceleration unless acted upon by a force
  2. The rate of change of momentum of an object is proportional to the resultant force on it – this can be written:  newtons laws momentum and impulse 4
  3. When two objects interact they exert equal and opposite forces on each other

The definition of momentum is:

blank spacelinear momentum = mass x velocity

Momentum has the symbol p, so in symbols this is:

newtons laws momentum and impulse 1

We can work out the units for momentum using the units for mass and velocity:

  newtons laws momentum and impulse 2

Change in momentum is called impulse. From Newton’s second law we can say:

newtons laws momentum and impulse 3

Which gives us that

blank spaceimpulse = force x time

Impulse is given the symbol J. This can be written in integral form:

newtons laws momentum and impulse 5

If we draw a force-time graph (force on the y axis and time on the x axis), the impulse is therefore the area under the graph.

From Newton’s third law we know that the forces in a collision are equal, and the times must also be equal.

newtons laws momentum and impulse 6

This means the impulse on each object is the same, so the change of momentum is the same. This tells us that momentum is conserved (that initial momentum = final momentum) which is useful in calculations about collisions.

Back to Contents: Physics: Mechanics

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