CalculateY
Quick Answer
A 10 kg object moving at 5 m/s has a momentum of 50 kg·m/s. A 1,500 kg car traveling at 20 m/s has a momentum of 30,000 kg·m/s.
Common Examples
| Input | Result |
|---|---|
| m = 10 kg, v = 5 m/s | p = 50.00 kg·m/s |
| m = 1,500 kg, v = 20 m/s | p = 30,000.00 kg·m/s |
| p = 500 kg·m/s, v = 10 m/s | m = 50.00 kg |
| p = 200 kg·m/s, m = 4 kg | v = 50.00 m/s |
| m = 0.145 kg, v = 40 m/s | p = 5.80 kg·m/s |
How It Works
The formula
The momentum formula describes an object’s quantity of motion:
\[p = m \times v\]Where:
- p = momentum in kilogram-meters per second (kg·m/s)
- m = mass in kilograms (kg)
- v = velocity in meters per second (m/s)
This equation can be rearranged to solve for any of the three variables:
\[m = \frac{p}{v} \qquad v = \frac{p}{m}\]Momentum is a vector quantity
Unlike kinetic energy, momentum has direction. A 10 kg ball moving east at 5 m/s has momentum +50 kg·m/s (if east is positive), while the same ball moving west at 5 m/s has momentum -50 kg·m/s. This directional property is what makes momentum central to collision and impact analysis.
Conservation of momentum
In any closed system (no external forces), total momentum is conserved. If two objects collide, their combined momentum before the collision equals their combined momentum after. This holds true for elastic collisions (where kinetic energy is also conserved), inelastic collisions (where objects stick together), and everything in between.
Impulse and momentum change
The impulse-momentum theorem states that the change in momentum equals force times time: F x t = m x Δv. This is why airbags and crumple zones work: they increase the time over which a collision occurs, reducing the peak force on the occupant while the total momentum change stays the same.
Units
In SI units, momentum is measured in kilogram-meters per second (kg·m/s). There is no special named unit for momentum, unlike energy (joules) or force (newtons). In some contexts, newton-seconds (N·s) are used, which are equivalent: 1 N·s = 1 kg·m/s.
Worked example
For a 10 kg object moving at 5 m/s: p = 10 x 5 = 50 kg·m/s. To find the mass of an object with p = 500 kg·m/s and v = 10 m/s: m = 500 / 10 = 50 kg. To find the velocity of a 4 kg object with p = 200 kg·m/s: v = 200 / 4 = 50 m/s. For a baseball (0.145 kg) thrown at 40 m/s (about 90 mph): p = 0.145 x 40 = 5.8 kg·m/s.
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