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, a 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

Elastic and inelastic are the two ends of one dial. Enter a second object and this page reports both, because the same pair of masses and velocities has a different answer depending on what the objects are made of. A perfectly elastic collision keeps every joule of kinetic energy; a perfectly inelastic one loses the most it is possible to lose while still conserving momentum. Real collisions land in between, and the coefficient of restitution is the number that says where. Momentum, though, comes out identical either way. That is the point of the conservation law, and it is why the panel prints the total before and after.

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.