Momentum Calculator

Momentum is the quantity of motion an object possesses — a measure of how hard it is to stop a moving object. Impulse is the change in momentum caused by a force applied over time.

Core formulas: Momentum: p = m × v Impulse: J = F × Δt = Δp = m × Δv Conservation of Momentum: m₁v₁ + m₂v₂ = m₁v₁′ + m₂v₂′

Where:

• p = momentum (kg·m/s)
• m = mass (kilograms)
• v = velocity (meters per second)
• J = impulse (N·s, equivalent to kg·m/s)
• F = applied force (Newtons)
• Δt = time duration of force application (seconds)
• Δv = change in velocity

The law of conservation of momentum: In a closed system with no external forces, the total momentum before a collision equals the total momentum after the collision. This is one of physics’ most fundamental conservation laws.

Worked example — Car collision: Car A: mass = 1,200 kg, velocity = 15 m/s (east) Car B: mass = 900 kg, velocity = 0 m/s (stationary) After perfectly inelastic collision (they stick together):

p_before = (1,200 × 15) + (900 × 0) = 18,000 kg·m/s Combined mass = 2,100 kg Final velocity = 18,000 ÷ 2,100 = 8.57 m/s east

Impulse example — catching a ball: A baseball (0.145 kg) pitched at 40 m/s is caught in 0.05 seconds. Impulse = 0.145 × 40 = 5.8 N·s Force = 5.8 ÷ 0.05 = 116 N average force on the catcher’s glove

Real-world applications: Car airbags (increasing Δt reduces peak force), rocket propulsion, billiards, sports collisions, and spacecraft trajectory planning all rely on momentum and impulse principles.