Momentum Calculator

Calculate momentum, mass, or velocity. Momentum is the product of mass and velocity.

Momentum Formula: p = mv Where: • p = momentum (kg*m/s) • m = mass (kilograms, kg) • v = velocity (meters per second, m/s) Note: Momentum is a vector quantity - direction matters! Rearrangements: • Mass: m = p/v • Velocity: v = p/m Conservation of Momentum: In isolated systems: sum(p_before) = sum(p_after) For two objects: m1*v1 + m2*v2 = m1*v1' + m2*v2'
Example 1 (Momentum): A 1500 kg car traveling at 25 m/s (~56 mph) p = 1500 * 25 = 37,500 kg*m/s This momentum must be reduced to zero to stop the car. Example 2 (Mass): An object has momentum 500 kg*m/s at velocity 10 m/s m = 500 / 10 = 50 kg Example 3 (Velocity): A 0.15 kg baseball has momentum 6 kg*m/s v = 6 / 0.15 = 40 m/s (~90 mph) Example 4 (Collision): Two carts collide and stick together (perfectly inelastic) Cart 1: m1 = 2 kg, v1 = 3 m/s -> p1 = 6 kg*m/s Cart 2: m2 = 3 kg, v2 = -1 m/s -> p2 = -3 kg*m/s Before: p_total = 6 + (-3) = 3 kg*m/s After: (m1 + m2)*v_f = 5*v_f = 3 -> v_f = 0.6 m/s Example 5 (Rocket): Rocket (1000 kg) ejects 10 kg exhaust at 2000 m/s By momentum conservation (starting from rest): 0 = 10 * 2000 + 990 * v_rocket v_rocket = -20,000/990 ~= -20.2 m/s (opposite direction)

What is momentum?

Momentum is the quantity of motion an object has, calculated as p = mv (mass × velocity). It's a vector quantity with both magnitude and direction. A heavy truck and fast bullet can have equal momentum despite different masses and velocities.

What are the units of momentum?

In SI units, momentum is measured in kg·m/s (kilogram-meters per second). In imperial units, it's slug·ft/s. There's no special name for the momentum unit like "joule" for energy.

What is the law of conservation of momentum?

In a closed system with no external forces, total momentum before an event equals total momentum after. This applies to collisions, explosions, and rocket propulsion. Mathematically: Σp_before = Σp_after.

How is momentum different from kinetic energy?

Momentum (p = mv) is a vector and is always conserved in isolated systems. Kinetic energy (KE = ½mv²) is a scalar and is only conserved in elastic collisions. They're related by KE = p²/(2m).

What is impulse and how does it relate to momentum?

Impulse is change in momentum: J = Δp = FΔt (force × time). A force applied over time changes momentum. This is why airbags work - they increase collision time, reducing force while keeping momentum change constant.

Can momentum be negative?

Yes, momentum is a vector. The sign indicates direction. In 1D motion, positive/negative indicates direction along an axis. In collisions, objects moving opposite directions have opposite-sign momenta.

What happens to momentum in elastic vs inelastic collisions?

Momentum is ALWAYS conserved in both elastic and inelastic collisions (in isolated systems). Kinetic energy is conserved only in elastic collisions. In inelastic collisions, some KE converts to heat, sound, or deformation.

How do you calculate velocity from momentum and mass?

Rearrange p = mv to get v = p/m. For example, if momentum is 1000 kg·m/s and mass is 50 kg, velocity = 1000/50 = 20 m/s. Lighter objects need higher velocity for the same momentum.

What is angular momentum?

Angular momentum (L = Iω or L = r × p) is rotational momentum. Like linear momentum, it's conserved in isolated systems. Examples: spinning ice skater pulls arms in to spin faster (constant L, smaller I means larger ω).

Why do rockets work in space with no air to push against?

Rockets work by conservation of momentum. Expelled exhaust gas gains momentum in one direction, so the rocket gains equal momentum in the opposite direction. No air needed - momentum is conserved in the rocket+exhaust system.

What are real-world applications of momentum?

Applications include: vehicle crash analysis, rocket design, ballistics, sports (bat hitting ball), particle physics (collider experiments), and explosion forensics. Momentum conservation is fundamental to all interactions.

How does momentum apply to photons?

Despite having zero mass, photons have momentum p = E/c = h/λ, where E is energy, c is light speed, h is Planck's constant, and λ is wavelength. This momentum is measurable (radiation pressure, laser cooling).