Newton's laws of motion:

Newton's First Law Every body continues in a state of rest or uniform motion in a straight line unless a net (external) force acts on it.

Newton's Second Law The rate of change of momentum of a body is directly proportional to the net force acting on the body, and the

momentum change takes place in the direction of the net force.

Newton's Third Law When object X exerts a force on object Y, object Y exerts a force

*of the same type* that is equal in magnitude and opposite in direction on object X.

The two forces ALWAYS act on

different objects and they form an

**action-reaction pair**.

Linear momentum and its conservation: Mass: is a measure of the amount of matter in a body, & is the

property of a body which resists change in motion.

Weight: is the force of gravitational attraction (exerted by the Earth) on a body.

Linear momentum: of a body is defined as the product of its mass and velocity ie p = m v

Impulse of a force (I): is defined as the product of the force and the time Δt during which it acts

ie I = F x Δt {for force which is const over the duration Δt}

For a

variable force, the impulse I = Area under the F-t graph { ∫Fdt; may need to “count squares”}

Impulse is

equal in magnitude to the change in momentum of the body acted on by the force.

Hence the change in momentum of the body is equal in mag to the area under a (net) force-time graph.

{

**Incorrect** to

**define** impulse as

*change in momentum*}

Force: is defined as the rate of change of momentum, ie F = [ m (v - u) ] / t = ma or F = v dm / dt

The {one} Newton: is defined as the force needed to accelerate a mass of 1 kg by 1 m s

^{-2}.

Principle of Conservation of Linear Momentum: When objects of a system interact, their total momentum before and after interaction are equal

if no **net** (external) force acts on the system.

- The total momentum of an
**isolated** system is constant -
**m**_{1} u_{1} + m_{2} u_{2} = m_{1} v_{1} + m_{2} v_{2} if net F = 0 {for **all** collisions }

NB: Total momentum

**DURING** the interaction/collision is also conserved.

(Perfectly) elastic collision: Both momentum & kinetic energy of the system are conserved.

Inelastic collision: Only momentum is conserved, total kinetic energy is not conserved.

Perfectly inelastic collision: Only momentum is conserved, and the particles stick together after collision. (i.e. move with the same velocity.)

For

**all ***elastic* collisions, u

_{1} – u

_{2} = v

_{2} – v

_{1} ie.

**relative speed of approach = relative speed of separation** or,

**½ m**_{1}u_{1}^{2} + ½ m_{2}u_{2}^{2} = ½ m_{1}v_{1}^{2} + ½ m_{2}v_{2}^{2}In inelastic collisions, total energy is conserved but Kinetic Energy may be converted into other forms of energy such as sound and heat energy.