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.

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.

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.