Momentum as signed motion
Momentum tells you how much signed motion a body has. A light body moving quickly and a heavy body moving slowly can have the same momentum. Its direction matters, so momentum is a vector: a quantity with both a size and a direction.
Combine mass with signed velocity
Definition
What is meant by linear momentum?
Model answer: The product of a body's mass and velocity. Its direction is the same as the direction of the velocity.
Symbols
- = linear momentum (kg m s⁻¹)
- = mass (kg)
- = signed velocity in the chosen direction (m s⁻¹)
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- At the same velocity, a larger mass gives a larger momentum magnitude.
- At the same mass, a larger speed gives more momentum magnitude.
- Reversing direction reverses the sign of momentum.
- A body at rest has zero momentum.
Key idea
Choose one positive direction before calculating
In one-dimensional motion, choose right, left, up or down as positive. Then turn every stated speed into a signed velocity before using .
Worked example
Two bodies moving towards one another
Right is positive. A 3 kg body moves right at 4 m s⁻¹ and a 5 kg body moves left at 2 m s⁻¹.
The total momentum is 2 kg m s⁻¹ to the right.
- Convert grams to kilograms by dividing by 1000. For example, .
- Convert kilometres per hour to metres per second by dividing by 3.6. For example, .
- Use for momentum in this course.
Common mistake
Calculate change as final minus initial
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Key idea
Up is positive. A 0.06 kg ball is moving downwards at 8 m s⁻¹ immediately before it rebounds from the floor. It moves upwards at 5 m s⁻¹ immediately after. Find the momentum before, the momentum after, the change in momentum and the magnitude of that change.
Show worked answer
All momentum values below are in kg m s⁻¹.
The change is upwards; its magnitude is 0.78 kg m s⁻¹.