PhysicsCalcs
Mechanics

Momentum Calculator

Calculate momentum (p = mv), impulse (J = Ft), change in momentum, or solve collisions with conservation of momentum. Step-by-step solutions with unit conversions.

Interactive calculator

Momentum Calculator

Calculate momentum (p = mv), impulse (J = Ft), change in momentum, or analyse collisions using conservation of momentum.

Try an example

Mass of the object

Velocity of the object

Your result will appear here.

Choose a calculation mode, fill in the known values, and click Calculate.

Quick Guide

  • Choose: find momentum, mass, velocity, impulse, or collision analysis.
  • Enter known values with units.
  • Click Calculate for step-by-step results.

Table of Contents

Key Takeaways

  • Momentum p = mv is a vector quantity (direction matters).
  • The SI unit of momentum is kg·m/s.
  • Impulse J = FΔt equals the change in momentum.
  • Total momentum is conserved in all collisions when no external forces act.
  • Elastic collisions conserve both momentum and kinetic energy.
  • Inelastic collisions conserve momentum but not kinetic energy.

What Is Momentum?

Momentum is a measure of an object’s tendency to keep moving. A heavy truck moving slowly can have the same momentum as a light bullet moving fast. This concept is central to understanding collisions, explosions, and rocket propulsion.

p = mv (Definition of Momentum)

p=mvp = mv

Momentum equals mass times velocity. Since velocity is a vector, momentum is also a vector — it has direction. The SI unit is kg·m/s (equivalent to N·s).

Impulse–Momentum Theorem

J=FΔt=Δp=m(v2−v1)J = F\Delta t = \Delta p = m(v_2 - v_1)

Impulse is the product of average force and time interval. It equals the change in momentum. Airbags work by increasing the collision time, reducing the average force on occupants.

Conservation of Momentum

m1v1+m2v2=m1v1′+m2v2′m_1 v_1 + m_2 v_2 = m_1 v'_1 + m_2 v'_2

In an isolated system (no external forces), total momentum before a collision equals total momentum after. This holds for elastic, inelastic, and perfectly inelastic collisions.

How to Use the Calculator

  1. Select the calculation mode matching your known values.
  2. Enter quantities with units.
  3. Click Calculate.
  4. Review momentum, impulse, or collision results with formula steps.

Example Calculations

10 kg at 5 m/s

p = 10 × 5 = 50 kg·m/s

Car: 1500 kg at 20 m/s

p = 30,000 kg·m/s = 30 kN·s

Collision: 5kg@3m/s + 10kg@1m/s (stick)

p = 25 kg·m/s, v′ = 25/15 = 1.67 m/s

Common Mistakes

  • Forgetting momentum is a vector — signs matter in 1D problems.
  • Using speed instead of velocity (dropping negative signs).
  • Confusing conservation of momentum with conservation of kinetic energy.
  • Applying momentum conservation when significant external forces act.

Accuracy and Limitations

These calculations assume classical mechanics (speeds « speed of light). At relativistic speeds, use relativistic momentum p = γmv. The calculator handles 1D collisions; 2D collisions require vector component analysis. This tool is for education and estimation.

FAQ

What is momentum?›

Momentum is mass times velocity: p = mv. It measures how hard it is to stop a moving object. A truck at 30 mph has far more momentum than a tennis ball at 30 mph.

Is momentum a vector or scalar?›

Momentum is a vector. It has both magnitude and direction (same direction as the velocity).

What is the impulse–momentum theorem?›

The impulse (average force × time) equals the change in momentum: J = FΔt = Δp = m(v₂ − v₁).

When is momentum conserved?›

Momentum is conserved when the net external force on the system is zero. In collisions, internal forces are large but external forces (gravity, friction) are often negligible during the brief collision.

What is the difference between elastic and inelastic collisions?›

Elastic: both momentum and kinetic energy are conserved (e.g., billiard balls). Inelastic: momentum is conserved but KE is not (some converts to heat, sound, deformation). Perfectly inelastic: objects stick together.

Can momentum be negative?›

Yes. Momentum is a vector. If you define rightward as positive, an object moving leftward has negative momentum.

How does momentum relate to Newton’s second law?›

Newton’s second law in its original form is F = dp/dt. For constant mass, this simplifies to F = ma.

Sources

  1. OpenStax University Physics – Linear Momentum
  2. HyperPhysics – Momentum
Manish Kumar

Author & technical reviewer

Manish Kumar

PhysicsCalcs tools are reviewed with an educational focus: clear formulas, transparent assumptions, and practical context for students and science learners.

Learn more about Manish