Momentum Formula
The momentum formula p = mv calculates an object's momentum from its mass and velocity.
Essential for collision and impulse problems.
The Formula
p = mv
Momentum is the product of an object's mass and its velocity. It is a vector quantity, meaning it has both magnitude and direction.
Variables
| Symbol | Meaning |
|---|---|
| p | Momentum (measured in kilogram meters per second, kg·m/s) |
| m | Mass of the object (measured in kilograms, kg) |
| v | Velocity of the object (measured in meters per second, m/s) |
Example 1
A 0.45 kg football is kicked at a velocity of 25 m/s. What is its momentum?
Identify the values: m = 0.45 kg, v = 25 m/s
Apply the formula: p = mv = 0.45 × 25
p = 11.25 kg·m/s
Example 2
A 2,000 kg truck has a momentum of 50,000 kg·m/s. How fast is it moving?
Rearrange the formula: v = p / m
Substitute: v = 50,000 / 2,000
v = 25 m/s
When to Use It
Use the momentum formula in problems involving motion and collisions.
- Calculating the momentum of moving objects
- Solving collision problems using conservation of momentum
- Determining the velocity or mass when momentum is known
- Analyzing impulse (change in momentum) during impacts
Key Notes
- Momentum is a vector — direction matters; a 1 kg ball at +5 m/s and another at −5 m/s have equal but opposite momenta; they cancel to zero total momentum in a perfectly symmetric head-on collision
- Conservation of momentum: in a closed system with no net external force, total momentum is constant — this is why rockets accelerate by expelling mass backward
- Impulse-momentum theorem: impulse (F × t) = change in momentum (Δp = mΔv) — airbags and crumple zones reduce injury by extending collision time, which reduces peak force for the same Δp
- Momentum and kinetic energy scale differently: KE = p²/(2m), so doubling speed doubles momentum but quadruples kinetic energy — relevant when comparing crash severity at different speeds