Mechanics⏱ 4 min read

Momentum

p = mv

What is the Momentum?

Momentum is the product of an object's mass and velocity, and it describes how hard it is to stop the object once it's moving. A heavy truck moving slowly can have more momentum — and be harder to stop — than a much lighter object moving fast, which is why momentum, not just speed, is what actually determines how forceful a collision will be.

One of the most important laws in physics follows from momentum: in a closed system, total momentum is conserved — the momentum before a collision equals the momentum after, even though individual objects' velocities may change dramatically. This single principle is how physicists analyze everything from billiard-ball collisions to rocket propulsion to particle physics experiments, since it holds even in situations far too complex to track every force directly.

Momentum is also historically the concept Newton's Second Law was originally built around — his own statement of the law was phrased in terms of the rate of change of momentum, F = dp/dt, and F = ma is the simplified version that applies specifically when an object's mass stays constant (see the Newton's Second Law page for that derivation).

What Each Variable Means

MomentumThe quantity of motion the object has. (kg·m/s)

MassThe mass of the moving object. (kilograms (kg))

VelocityThe speed and direction of the object. (m/s)

When to Use It

Calculating an object's momentum from its mass and velocity
Analyzing collisions using conservation of momentum
Comparing how difficult two different moving objects are to stop

Step-by-Step Example

Problem: A 70 kg person runs at 6 m/s. What is their momentum?

Identify the known values

Mass and velocity are both given.

m = 70 kg, v = 6 m/s

Apply the formula

Multiply mass by velocity.

p = 70 × 6

✓

Answer: p = 420 kg·m/s

Interactive Calculator

m (mass) (kg)v (velocity) (m/s)

Result will appear here

Common Mistakes

Mistake: Treating momentum as a scalar and ignoring direction.
Fix: Momentum is a vector — it has direction, same as velocity. In a collision problem, momentum in opposite directions should be given opposite signs, not just added as magnitudes.
Mistake: Confusing momentum with kinetic energy.
Fix: Momentum (p = mv) scales linearly with velocity; kinetic energy (KE = ½mv²) scales with velocity squared — they behave very differently as speed changes.

Practice Questions

A 1,200 kg car moves at 25 m/s. What is its momentum?
What velocity gives a 5 kg object a momentum of 40 kg·m/s?
Hint: Rearrange p = mv to solve for v.

Frequently Asked Questions

What is conservation of momentum?

In a closed system with no external forces, total momentum before an event (like a collision) equals total momentum after: m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'.

Is momentum the same in every reference frame?

No — momentum depends on velocity, which is relative to whatever frame you measure it from. Different observers moving at different speeds will calculate different momentum values for the same object.