# 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

*impulse as*

**define***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
system is constant__isolated__ -
**m**if net F = 0 {for_{1}u_{1}+ m_{2}u_{2}= m_{1}v_{1}+ m_{2}v_{2}**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.