Mass, Inertia, and Momentum Inertia is the reluctance of a body to change whether it is moving or not and is related to its mass. Once a body is moving the momentum of the body is a product of its mass multiplied by its velocity.

Mass

The mass of a body refers to the amount of substance that it is made up of and is measured in kilograms (Kg). For example, a footballer is made up of bones, muscle, fat, connective tissue etc and all of that ‘substance’ will have a mass of 100 Kg for example. When speaking scientifically this is is not the same as weight. Although we talk about a players ‘weight’ and measure it on bathroom scales, weight is a force and from Newton’s 2nd law (force = mass x acceleration due to gravity). If the same footballer was placed on the moon her mass would still be 90.8Kg but her weight would be much less because gravity is less.

Inertia

Inertia is the bodies resistance to change in motion and is related to mass. If you want to get an object with a large mass moving you have to apply more force than if you want to get a tiny object moving. It really is that simple. Likewise, if you want to slow down or stop a heavy object you will need to apply a greater force to it than if you want to slow down a small object.

Examples:

• Elite cyclist Sir Bradley Wiggins had a mass of around 69Kg. The force Sir Bradley needs to apply to get his bike moving is a lot less than if boxer Mike Tyson (109Kg) sat on the saddle.
• If you kick a football (mass 0.41Kg – 0.45Kg according to law 2 of the game) you need to apply a smaller force than if you tried to take a penalty kicking an 8Kg medicine ball (don’t try that at home!).
• A 100m sprinter needs to apply a larger force when accelerating from the start to build up speed than they do during the middle of the race where their speed is more constant. After they cross the line large forces are needed to slow the sprinter down again which is why you should always slow down gradually to avoid those large forces causing injuries.

Momentum

Momentum is a measure of the amount of motion a body has and is measured in units of kilogram metres per second (Kgm/s).

momentum (Kgm/s) = mass (Kg) x velocity (m/s)

Momentum is important in sport, particularly contact sports where collisions are involved. The more momentum a rugby player has the harder it is to stop her. The more momentum the bobsleigh has at the start of the run, the faster it is likely to go. Here are some examples:

• A rugby player mass 90Kg is running at 10m/s. What is the player’s momentum?

momentum = 90Kg 10m/s = 900Kgm/s

• A 4 man bobsleigh crew mass 630Kg (the maximum allowable by the rules) is travelling at 42.5m/s (the current world record at 153Km/hour). What is its momentum?

momentum = 630Kg x 42.5m/s = 26 775 Kgm/s

• How fast does the rugby player have to run to have the same speed as the bobsleigh travelling at 2m/s?

bobsleigh momentum = 630Kg x 2m/s = 1260 Kgm/s

rugby player momentum (1260 Kgm/s) = 90Kg x velocity therefore….. velocity = 1260/90 = 14m/s