Momentum Calculator

Find momentum p = mv, the impulse from a force over time, and the velocities after an elastic or perfectly inelastic collision.

Momentum

p = m × v
Solve for
p
Momentum
5.8kg·m/s
1 sig figs: 6
≡
Same value in
580,000 g·cm/s
5.8 N·s
  1. Rearrange: p = m × v
  2. Substitute: m = 0.145 kg, v = 40 m/s (converted to SI units first).
  3. Result: p = 5.8 kg·m/s, rounded to 1 significant figures because the least precise input has 1.

Impulse

J = F × Δt = Δp
Solve for
J
Impulse (change in momentum)
12N·s
1 sig figs: 10
≡
Same value in
12 kg·m/s
1,200,000 g·cm/s
  1. Rearrange: J = F × Δt
  2. Substitute: F = 2400 N, Δt = 5 ms (converted to SI units first).
  3. Result: J = 12 N·s, rounded to 1 significant figures because the least precise input has 1.

One-dimensional collision

Right is positive. A negative velocity means moving left.

v₁
Velocity 1 after
0.3333m/s
v₂
Velocity 2 after
4.333m/s
Σp
Total momentum (conserved)
5kg·m/s
ΔKE
Kinetic energy lost
1.776 × 10⁻¹⁵J
9.5 J before

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0/1500

Worked example

A 0.145 kg baseball thrown at 40 m/s has p = 0.145 × 40 = 5.8 kg·m/s. If the bat sends it back at 50 m/s, the change in momentum is 0.145 × (50 − (−40)) = 13.1 kg·m/s. Over 1.0 ms of contact that is an average force of 13 000 N.

Frequently asked questions

What is the momentum formula?
p = mv, mass (kg) times velocity (m/s), in kg·m/s. Momentum is a vector: it has the direction of the velocity.
What is conservation of momentum?
In a closed system with no external force, total momentum before a collision equals total momentum after: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂. It holds for every kind of collision.
What is the difference between elastic and inelastic collisions?
In an elastic collision kinetic energy is also conserved (billiard balls, approximately). In an inelastic collision some kinetic energy becomes heat, sound and deformation. Perfectly inelastic means the objects stick together.
What is impulse?
Impulse J = FΔt, force times the time it acts, and it equals the change in momentum. Airbags and crumple zones increase Δt so the same change in momentum needs a smaller force.