This tool calculates linear momentum and impulse, the two closely linked quantities at the heart of collision and motion physics. It is for students, teachers, and anyone working through classical mechanics problems.
How it works
Two modes share one core idea — momentum is mass in motion, and impulse is the force that changes that momentum over time:
- Momentum: p = m × v, with mass m in kilograms and velocity v in metres per second, giving the result in kg·m/s.
- Impulse: J = F × t = Δp, with force F in newtons and contact time t in seconds, giving newton-seconds (N·s).
The impulse–momentum theorem ties them together: the impulse applied to an object equals the change in its momentum. Because 1 N·s = 1 kg·m/s dimensionally, impulse and momentum share the same unit, which makes the theorem elegant: whatever impulse you apply, that is exactly how much the momentum changes.
Worked examples
Example 1 — find the momentum of a moving object: A 10 kg shopping trolley rolls at 5 m/s. Its momentum is: p = 10 × 5 = 50 kg·m/s
Doubling the velocity (10 m/s) doubles the momentum (100 kg·m/s). Doubling the mass has the same effect — momentum scales equally with both.
Example 2 — find the impulse needed to stop an object: To stop the same trolley (Δp = 50 kg·m/s) using a braking force of 25 N: t = Δp ÷ F = 50 ÷ 25 = 2 seconds
The same impulse (50 N·s) can be delivered as a large force over a short time or a small force over a longer time — the final change in momentum is identical. This is why crumple zones in cars extend the collision duration to reduce peak force on passengers: same impulse, longer time, lower peak force.
Example 3 — sports application: A cricket ball of mass 0.16 kg reaches the batsman at 35 m/s. The batsman deflects it back at 25 m/s. Treating the sign for direction (incoming negative, outgoing positive):
Δp = 0.16 × (25 − (−35)) = 0.16 × 60 = 9.6 N·s of impulse applied by the bat.
Key relationships and common mistakes
Momentum is a vector. It has direction as well as magnitude. This calculator handles magnitudes; for problems where direction matters (collisions, 2D projectiles), resolve each axis separately and sum components.
Conservation of momentum. In an isolated system (no external forces), total momentum before a collision equals total momentum after. This calculator does not model collisions directly — it handles single-object p = mv — but the impulse mode lets you find the change in momentum imparted by a known force.
Confusing impulse with force. Impulse is force × time, not force alone. A large force applied very briefly can produce less impulse (and less change in momentum) than a moderate force sustained for a longer period. The distinction matters in impact problems.
| Quantity | Symbol | Formula | Units |
|---|---|---|---|
| Momentum | p | m × v | kg·m/s |
| Impulse | J | F × t | N·s |
| Change in momentum | Δp | J = F × t | kg·m/s |
Every calculation runs locally in your browser and nothing is uploaded.