# Dynamics

#### 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
• m1 u1 + m2 u2 = m1 v1 + m2 v2 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, u1 – u2 = v2 – v1

ie. relative speed of approach = relative speed of separation

or, ½ m1u12 + ½ m2u22 = ½ m1v12 + ½ m2v22

In inelastic collisions, total energy is conserved but Kinetic Energy may be converted into other forms of energy such as sound and heat energy.