Momentum and Newton's Laws

An object will remain at rest or keep traveling at constant velocity unless it is acted upon by an external force.

An object will move away from a stationary position, change direction or change speed only if acted on by a resultant (net) force.

An object travelling at constant velocity has constant momentum. The momentum of an object remains constant unless the object experiences an external force.

The net force acting on an object is directly proportional to the rate of change of the linear momentum* of that object. The net force and the change in momentum are in the same direction.

* Linear momentum: the mass of an object multiplied by its velocity. It is a vector quantity which means it has mass and direction. Unit - N/s

F∝m(v-u)/t                                                      F∝ma (this is also written as F=ma when mass is constant)

Net force ∝ rate of change of momentum

F∝Δp/Δt

When two bodies interact, the forces they exert on each other are equal and opposite.

The two forces exerted by the objects on one another are often referred to as action and reaction. This does not mean that one force is exerted before the other - both occur at the same time.

The two forces:

• act on different bodies
• are of equal magnitude
• are opposite in direction
• are of the same type (both magnetic / both gravitational / both electrical)

These forces do not cancel each other out because although they are equal, they are acting upon different objects.

Momentum = mass x velocity

p = mv

Conservation of momentum: For a closed system, in any specified direction, the total momentum before an interaction (e.g. collision) is equal to the total momentum after the reaction.

In all interactions, momentum and total energy are conserved.

Impulse: The change in momentum of a body

A perfectly elastic collision is one in which no momentum or KE is lost. An inelastic collision is one in which momentum is conserved but KE is lost.

In a perfectly elastic collision, KE is conserved whereas in an inelastic collision, KE is transformed into other forms of energy (heat, sound). Most collisions are inelastic.