Classical Mechanics

Momentum Calculator

Calculate momentum, mass or velocity. Shows kinetic energy. Formula: p = mv.

Mass (m) — kg

Velocity (v) — m/s

Result

p = mv

Kinetic Energy

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Step-by-Step Solution

What is Momentum?

Momentum is a vector quantity that describes how difficult it is to stop a moving object. A heavy truck moving slowly can have the same momentum as a fast-moving bicycle. The law of conservation of momentum — in any isolated system, total momentum never changes — is one of the most important laws in physics.

p = mv

p = momentum (kg·m/s) | m = mass (kg) | v = velocity (m/s)

Variables Explained

Symbol	Name	Unit	Description
p	Momentum	kg·m/s	Vector — direction matters. Positive = forward, negative = backward
m	Mass	kg	Amount of matter; always positive
v	Velocity	m/s	Speed with direction; can be negative
J	Impulse	N·s	Change in momentum: J = Δp = FΔt

💡 Momentum is conserved in all collisions. In elastic collisions, kinetic energy is also conserved. In inelastic collisions, some KE is lost to heat and sound.

Conservation of Momentum

When two objects collide in an isolated system: m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'. This equation allows us to predict the outcome of collisions without knowing the exact forces involved. It works for everything from subatomic particles to galaxy collisions.

Frequently Asked Questions

What is impulse?

Impulse J = FΔt = Δp. It is the change in momentum caused by a force over time. A large force for a short time or a small force for a long time can produce the same impulse. Car airbags work by extending collision time to reduce the peak force.

Is momentum always conserved?

In a closed system with no external forces, yes — always. In real situations, friction and gravity can change total momentum of a subset of objects. For collisions (very short times), external forces are negligible and momentum is well conserved.

What is the difference between momentum and kinetic energy?

Momentum p = mv is a vector and is always conserved in collisions. KE = ½mv² is a scalar and is only conserved in elastic collisions. Two objects can have equal momentum but very different kinetic energies if their masses differ.