Linear Momentum

Linear momentum, p, is defined as the product of mass and velocity

$p = m v$

Where:
- p = linear momentum in kilogram metres per second (kg m s^-1)
- m = mass in kilograms (kg)
- v = velocity in metres per second (m s^-1)

Momentum is a vector quantity; it has both magnitude and direction
It can have a positive or negative value which describes its direction in a one dimensional plane
- If an object travelling to the right has positive momentum, an object travelling to the left (in the opposite direction) has a negative momentum

Momentum of a ball hitting a wall

Negative momentum, downloadable AS & A Level Physics revision notes

When the ball is travelling in the opposite direction, its velocity is negative. Since momentum = mass × velocity, its momentum is also negative

Worked example

A tennis ball of mass, m = 60 g travels at a velocity, v = 75 m s^-1. A brick of mass, m = 3 kg travels at a velocity, v = 1.5 m s^-1.

Determine which object has the most momentum.

3-1-3-we-momentum-comparison-question-cie-new

Answer:

Step 1: List the known quantities and convert to SI units

Mass of tennis ball, $m_{T} = 0.06 kg$
Velocity of tennis ball, $v_{T} = 75 m s^{- 1}$
Mass of brick, $m_{B} = 3 kg$
Velocity of brick, $v_{B} = 1.5 m s^{- 1}$

Step 2: Determine the momentum of the tennis ball

$p_{T} = m_{T} \times v_{T}$

$p_{T} = 0.06 \times 75$

$p_{T} = 4.5 kg m s^{- 1}$

Step 3: Determine the momentum of the brick

$p_{B} = m_{B} \times v_{B}$

$p_{B} = 3 \times 1.5$

$p_{B} = 4.5 kg m s^{- 1}$

Step 4: State which object has the most momentum

Both objects have the same momentum
- Even though the brick has a greater mass, it has a much lower velocity than the tennis ball

Examiner Tip

Remember to convert the values given into SI units. It is good practice to do this before the calculation.

If the mass is given in grams, convert to kg by dividing the value by 1000
If the velocity is given in km s⁻¹, convert to m s⁻¹ by multiplying the value by 1000

Like with Force and Acceleration, the direction you consider positive is your choice, as long you are consistent throughout the calculation.

Linear Momentum (CIE AS Physics)

Revision Note

Linear momentum

Momentum of a ball hitting a wall

Worked example

Examiner Tip

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Author: Leander