Calculator · Engineering Mechanics
Impulse–Momentum Calculator
Linear momentum p = m·v and impulse J = Δp for a planar particle. Momentum and impulse share SI base dimensions but are never interchanged here, and neither is ever reported as a velocity.
Calculation
Particle, initial velocity and impulse
Results
| Initial momentum p₁ = m·v₁ | (2, 0) kg·m/s |
|---|---|
| Impulse J | (4, 6) N·s |
| Final momentum p₂ = p₁ + J | (6, 6) kg·m/s |
| Final velocity v₂ = p₂/m | (3, 3) m/s |
| Initial speed |v₁| | 1 m/s |
| Final speed |v₂| | 4.2426 m/s |
| |J| | 7.2111 N·s |
| Direction of J from +x | 56.31° |
Technical reference
p = m·v
J = F·Δt (constant force only)
J = Δp = p₂ − p₁
- p
- linear momentum[kg·m/s]
- m
- particle mass[kg]
- v
- velocity[m/s]
- J
- impulse[N·s]
- F
- constant force[N]
- Δt
- duration[s]
The general definition J = ∫F dt is implemented here only for a constant force, where it reduces to J = F·Δt; the momenta-based mode instead computes J directly as Δp. Momentum and impulse share SI base dimensions but are kept as distinct quantities and neither is ever reported as a velocity.
This is linear momentum of a particle only, with no angular term. For a rigid body, angular momentum and angular impulse also apply, see the Rigid-Body Impulse–Momentum Calculator.
Assumptions
- · Point particle with a constant mass greater than zero.
- · J = F·Δt applies to a CONSTANT force over the stated duration.
- · Momentum [kg·m/s] and impulse [N·s] are distinct quantities and are never presented as a velocity.
- · The impulse is instantaneous in the momentum balance: no trajectory is implied by it.
Continue
Only the force-and-duration mode defines a complete motion model, so it is the only mode that continues into the Particle Motion Lab.