Linear momentum
- Linear momentum, p, is defined as the product of mass and velocity
- 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
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.
Answer:
Step 1: List the known quantities and convert to SI units
- Mass of tennis ball,
- Velocity of tennis ball,
- Mass of brick,
- Velocity of brick,
Step 2: Determine the momentum of the tennis ball
Step 3: Determine the momentum of the brick
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.