Momentum

Definition of Momentum

Momentum is a measure of how much motion an object has. It depends on two factors:

• Mass of the object (how much matter it contains)
• Velocity of the object (speed in a specific direction)

Momentum is a vector quantity, which means it has both size and direction. The direction of momentum is the same as the direction of the velocity.

Momentum is measured in kilogram metres per second (kg·m/s).

For instance, if a footballer kicks a 0.5 kg ball moving at 20 m/s to the right, the momentum is:

Conservation of Momentum

The law of conservation of momentum states that in a closed system (where no external forces act), the total momentum before an event is equal to the total momentum after the event.

This is especially important in collisions or explosions where objects interact.

Mathematically:

A closed system means no external forces like friction or air resistance affect the objects during the interaction.

For example, if two ice skaters push off each other on frictionless ice, their momenta after pushing off will be equal in size but opposite in direction, so total momentum remains zero if they started at rest.

Collisions

When two objects collide, momentum is transferred between them. The total momentum of the system remains constant if no external forces act.

There are two main types of collisions:

• Elastic collisions: Both momentum and kinetic energy are conserved. The objects bounce off each other without permanent deformation or heat generation.
• Inelastic collisions: Momentum is conserved, but kinetic energy is not. Some energy is converted into other forms like heat or sound, and objects may stick together.

Examples of collisions:

• Car crashes: Usually inelastic collisions where cars crumple and kinetic energy is lost as heat and sound.
• Sports: A tennis ball bouncing off a racket is an elastic collision, while a rugby tackle is more inelastic.

During a collision, one object loses momentum while the other gains an equal amount, keeping total momentum constant.

For example, if a 2 kg ball moving at 3 m/s collides head-on with a stationary 3 kg ball, momentum is transferred between them during the collision.

Force and Momentum

Force is related to how quickly momentum changes. The greater the force, the faster the momentum changes.

This relationship is given by the formula:

This means that if an objects momentum changes rapidly, a large force acts on it.

The product of force and the time over which it acts is called impulse:

Impulse explains why safety features in vehicles are designed to increase the time over which momentum changes, reducing the force experienced:

• Seat belts: Stretch slightly to increase stopping time.
• Airbags: Inflate to cushion impact and extend the time of collision.
• Crash barriers: Deform to absorb energy and increase collision time.

By increasing the time taken for momentum to change, the force on passengers is reduced, lowering injury risk.

For example, if a cars momentum changes by 2000 kg·m/s over 0.5 seconds during a crash, the average force is: