Momentum
Forces & Motion
What momentum is
- Momentum is a property carried by every moving object, telling you how hard it would be to stop or to turn
- A heavier object moving at the same speed has more momentum than a lighter one; the same object moving faster has more momentum than when it was moving slowly
- A stationary object has zero , so at v = 0, p = 0
The equation
p = m × v
- where:
- p = momentum (kg m/s)
- m = mass (kg)
- v = velocity (m/s)
- The SI unit follows from the equation: kilograms × metres per second → kg m/s
Common exam question
Stating and using momentum = mass × velocity
Question: State the formula linking momentum, mass and velocity, then use it to find a momentum, mass or velocity, often as a "show that" (1 mark, then 2–3 marks for the calculation).
Set in 4 of the 24 papers, two of which first ask for the formula as a separate mark: write momentum = mass × velocity or p = m × v. Any correct rearrangement is accepted, but use p for momentum; m or M for momentum is ignored. The calculation earns one mark for the substitution and one for the evaluation; a third mark, when there is one, is for the rearrangement or for writing the formula down unasked.
In a "show that" question give the value to two or more significant figures before comparing it with the target: one scheme gives two of three marks to a value cut short to the wrong two figures. Convert km/s to m/s first; a power-of-ten slip costs a mark.
Momentum is a vector
- Velocity carries a direction, and momentum is mass × velocity, so is a vector quantity that points the same way the object is moving
- When working with momentum on a straight line:
- Pick one direction as positive (rightwards and upwards are the usual conventions)
- The opposite direction is then negative
- A momentum that comes out negative simply means the object is moving the opposite way to the direction you chose as positive
When momentum changes
- An object's momentum changes whenever any of the following happen:
- its velocity increases or decreases (any acceleration along the line of motion)
- its direction of travel changes (which is also an acceleration, even at constant speed)
- its mass changes (such as a rocket burning off fuel)
Worked example
Calculating momentum: p = mv
A 3.0 kg ball rolls along a track at 8.0 m/s. Calculate the momentum of the ball.
Solution:
- Recall the formula: p = m × v
- Substitute: p = 3.0 × 8.0
- p = 24 kg m/s (in the direction of motion)