Calculation Results


This page explains how to calculate linear momentum from mass and velocity. It also shows how to find mass or velocity if you know momentum and one other value.

Core idea

Linear momentum is the product of mass and velocity. It tells how hard it is to stop a moving object.

Basic formula

p = m × v

Where:

  • p is momentum in kilogram metre per second (kg·m/s)
  • m is mass in kilograms (kg)
  • v is velocity in metres per second (m/s)

Rearranged formulas

Find mass: m = p ÷ v (v ≠ 0).

Find velocity: v = p ÷ m (m ≠ 0).

How to use

  1. Put mass in kilograms and velocity in m/s.
  2. Multiply to get momentum in kg·m/s.
  3. If you need mass or velocity, divide momentum by the known value.
  4. Keep units consistent. Convert grams to kg and km/h to m/s before using formulas.

Unit conversions

  • 1 kg = 1000 g
  • To convert km/h to m/s: divide by 3.6. Example: 36 km/h = 10 m/s.
  • Momentum units: kg·m/s (same as N·s).

Worked examples

Example 1 — calculate momentum

Mass = 2 kg. Velocity = 3 m/s.

Momentum: p = 2 × 3 = 6 kg·m/s.

Example 2 — find velocity

Momentum = 20 kg·m/s. Mass = 4 kg.

Velocity: v = 20 ÷ 4 = 5 m/s.

Example 3 — find mass

Momentum = 50 kg·m/s. Velocity = 10 m/s.

Mass: m = 50 ÷ 10 = 5 kg.

Conservation of momentum

In a closed system with no external force, total momentum stays the same before and after collisions. Use Σp_before = Σp_after to solve collision problems.

Common mistakes

  • Mixing units. Convert to kg and m/s first.
  • Dividing by zero when you use the rearranged formula. Check your input.
  • For collisions, forgetting external forces. Momentum is conserved only if external forces are negligible.
  • Using speed instead of velocity in direction-sensitive problems. Velocity includes direction; speed does not.

Quick tips

  • Keep direction signs for vector momentum. Use + and − for opposite directions.
  • For 1D problems, treat momentum as positive or negative based on chosen axis.
  • In elastic collisions, both momentum and kinetic energy are conserved. In inelastic collisions, only momentum is conserved.
  • Momentum and impulse are related: Impulse = Δp = F_avg × Î”t.

FAQ

What is momentum?

Momentum is mass times velocity. It measures how hard it is to stop a moving object.

What units does momentum use?

Momentum uses kg·m/s. This is the same as newton-second (N·s).

How is momentum different from kinetic energy?

Momentum depends linearly on velocity (p = m v). Kinetic energy depends on the square of velocity (KE = ½ m v²). They show different physical aspects.

Is momentum a vector?

Yes. It has size and direction. Add components to handle 2D or 3D problems.

What is impulse?

Impulse changes momentum. It equals average force times time, and equals the change in momentum: J = F_avg × Î”t = Δp.

How do I handle collisions?

Write total momentum before the event and set it equal to total momentum after. Use signs for direction. For elastic collisions also use energy conservation.

Can I use momentum for rockets?

Yes. Rocket motion uses momentum and mass flow. The rocket equation comes from momentum balance with expelled mass.

What if mass changes during motion?

Use the variable-mass form and account for mass flow. For simple problems use momentum conservation on the whole system including ejected mass.

How precise should I be with decimals?

Two or three significant figures are fine for typical school problems. Use more if your data is precise.

How to check my answer?

Check units. Do a reasonableness check. If a small mass has huge momentum, re-check velocity units.

Can momentum be negative?

Yes. Negative momentum means motion in the chosen negative direction.

Why use velocity not speed?

Velocity has direction. Momentum requires direction for correct vector addition and conservation checks.

What is center-of-mass momentum?

Total momentum equals total mass times center-of-mass velocity: Σp = M_total × v_cm.