Inertia and momentum – Higher

Inertia

The only way to change the velocity of an object is to apply a force over a period of time.

In some cases, it takes a long time to change the velocity significantly. In these cases, the object seems reluctant to have it’s speed changed.

The tendency of an object to continue in its current state (at rest or in uniform velocity) is called inertia.

All objects have inertia. Whether they are moving or not.

Inertial mass

The ratio of force over acceleration is called inertial mass. Inertial mass is a measure of how difficult it is to change the velocity of an object. The inertial mass can be measured using this rearrangement of Newton's second law:

\text{m} = \frac{\text{F}}{\text{a}}

Momentum

Momentum is a property of moving objects and is useful when analysing collisions.

Momentum is the product of mass and velocity. Momentum is also a vector quantity – this means it has both a magnitude and an associated direction.

For example, an elephant has no momentum when it is standing still. When it begins to walk, it will have momentum in the same direction as it is travelling. The faster the elephant walks, the larger its momentum will be.

Calculating momentum

Momentum can be calculated using the equation:

momentum = mass × velocity

\text{p} = \text{mv}

This is when:

  • momentum ( \text{p}) is measured in kilogram metres per second (kg m/s)
  • velocity ( \text{v}) is measured in metres per second (m/s)
  • mass ( \text{m}) is measured in kilograms (kg)

Example

A lorry has a mass of 7,500 kg. It travels south at a speed of 25 m/s. Calculate the momentum of the lorry.

\text{p} = \text{mv}

= 7,500 × 25

= 187,500 kg m/s (south)

Question

An ice skater has a mass of 60 kg and travels at a speed of 15 m/s. Calculate the momentum of the skater.

\text{p} = \text{mv}

= 60 × 15

= 900 kg m/s

Conservation of momentum

In a closed system:

total momentum before an event = total momentum after the event

A 'closed system' is something that is not affected by external forces. This is called the principle of conservation of momentum. Momentum is conserved in collisions and explosions.

Conservation of momentum explains why a gun or cannon recoils backwards when it is fired. When a cannon is fired, the cannon ball gains forward momentum and the cannon gains backward momentum. Before the cannon is fired (the 'event'), the total momentum is zero. This is because neither object is moving. The total momentum of the cannon and the cannon ball after being fired is also zero, with the cannon and cannon ball moving in opposite directions.

Calculations involving collisions

Collisions are often investigated using small trolleys. The following diagrams show an example.

There are two trolleys, red and blue, The blue trolley is heading towards the stationary red one. There is an arrow above the trolley to indicate motion and direction.

Before collision

You can use the principle of conservation of momentum to calculate the velocity of the combined trolleys after the collision.

Example calculation

Calculate the velocity of the trolleys after the collision in the example above.

First calculate the momentum of both trolleys before the collision:

2 kg trolley = 2 × 3 = 6 kg m/s

4 kg trolley = 8 × 0 = 0 kg m/s

Total momentum before collision = 6 + 0 = 6 kg m/s

Total momentum (p) after collision = 6 kg m/s (because momentum is conserved)

Mass ( \text{m}) after collision = 10 kg

Next, rearrange \text{p} = \text{mv} to find \text{v}:

\text{v} = \frac{\text{p}}{\text{m}}

= 6 ÷ 10

= 0.6 m/s

Note that the 2 kg trolley is travelling to the right before the collision. As its velocity and the calculated velocity after the collision are both positive values, the combined trolleys must also be moving to the right after the collision.

Move on to Test
next