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Momentum Calculator

Momentum Calculator

Calculate linear momentum and solve elastic or perfectly inelastic collision problems with unit conversions and visual comparisons.

What Is Momentum?

Momentum is a fundamental concept in physics that describes the quantity of motion an object has. It is defined as the product of an object's mass and velocity:

Momentum Formula: p = mv where p is momentum, m is mass, and v is velocity

Momentum is a vector quantity, meaning it has both magnitude and direction. One of the most important principles in physics is the conservation of momentum: in any closed system, the total momentum before an interaction equals the total momentum after.

Why Momentum Matters

Collision Analysis

Understanding what happens when objects collide, essential for accident reconstruction and safety engineering

Vehicle Safety

Designing crumple zones and airbags to protect passengers by managing momentum transfer

Sports Science

Analyzing impacts in baseball, tennis, football, and other sports to optimize performance

Rocket Propulsion

Explaining how rockets accelerate in space through conservation of momentum

How to Use the Momentum Calculator

Linear Momentum Mode

1

Select Mode

Click the Linear Momentum tab at the top of the calculator

2

Choose Variable

Select what you want to solve for: Momentum, Mass, or Velocity

3

Enter Values

Input the two known values and select their appropriate units from the dropdown menus

4

Instant Results

The result appears automatically as you type — no need to click calculate

5

Review Analysis

View the formula breakdown, unit conversions, and comparison chart below the calculator

Collision Mode

1

Switch Mode

Click the Collision tab to access collision analysis tools

2

Select Collision Type

Choose between Elastic (objects bounce) or Perfectly Inelastic (objects stick together)

3

Input Object Data

Enter the mass and initial velocity for both objects involved in the collision

4

Set Direction

Use negative values for objects moving in the opposite direction (e.g., head-on collision)

5

Analyze Results

View final velocities, formula steps, and detailed momentum/energy analysis

Direction matters: Use negative velocity values to indicate opposite directions. For example, if Object 1 moves right at +10 m/s and Object 2 moves left, enter -10 m/s for Object 2.

Understanding the Results

Formula Display

Shows the complete calculation with your actual input values substituted into the equation

  • Step-by-step breakdown
  • Clear variable substitution
  • Final result highlighted

Unit Conversions

Click to expand and see your result converted to all supported unit systems

  • Metric and imperial units
  • Scientific notation options
  • One-click conversion access

Comparison Bars

Visualize your result against real-world momentum values for context

  • Tennis ball momentum
  • Walking person
  • Moving car and train

Energy Analysis

For collisions, see momentum conservation and kinetic energy changes

  • Before/after comparison
  • Energy loss percentage
  • Conservation verification

Features

Linear Momentum Calculator

Calculate any variable in the momentum equation p = mv by providing the other two. The calculator supports multiple unit systems for maximum flexibility:

Momentum Units

  • kg·m/s (SI standard)
  • N·s (Newton-seconds)
  • g·cm/s (CGS system)
  • lb·ft/s (Imperial)
  • slug·ft/s (Engineering)

Mass Units

  • kg (kilogram)
  • g (gram)
  • mg (milligram)
  • lb (pound)
  • oz (ounce)
  • ton (metric)
  • slug

Velocity Units

  • m/s (meters/second)
  • km/h (kilometers/hour)
  • mph (miles/hour)
  • ft/s (feet/second)
  • knots (nautical)

Collision Calculator

Solve collision problems between two objects with comprehensive physics analysis:

Elastic Collision

Objects Bounce

Both momentum and kinetic energy are conserved. Objects separate after impact with calculated final velocities.

  • Momentum: Conserved 100%
  • Kinetic Energy: Conserved 100%
  • Example: Billiard balls, atomic particles
  • Result: Two separate final velocities
Perfectly Inelastic

Objects Stick

Objects stick together after impact. Momentum is conserved but kinetic energy is partially lost to heat and deformation.

  • Momentum: Conserved 100%
  • Kinetic Energy: Partially lost
  • Example: Car crashes, clay balls
  • Result: Combined final velocity

Visual Analysis

Formula Breakdown

See the step-by-step calculation with your actual input values clearly displayed

  • Variable substitution shown
  • Mathematical operations explained
  • Final answer highlighted

Unit Conversion Table

Instantly view results in all supported units with expandable conversion panel

  • All unit systems included
  • Precise conversion factors
  • Copy-friendly format

Comparison Chart

Compare your momentum with real-world references for better understanding

  • Tennis ball (0.06 kg at 50 m/s)
  • Walking person (70 kg at 1.4 m/s)
  • Moving car (1500 kg at 25 m/s)
  • Train (100,000 kg at 30 m/s)

Before/After Bars

Visualize how momentum and kinetic energy change in collisions

  • Momentum conservation verified
  • Energy loss calculated
  • Color-coded visualization

Frequently Asked Questions

What is the difference between elastic and inelastic collisions?

In an elastic collision, both momentum and kinetic energy are conserved — the objects bounce off each other with no energy lost to heat or deformation. This is an idealized scenario that occurs approximately with billiard balls or atomic particles.

In a perfectly inelastic collision, the objects stick together after impact and move as one combined mass. Momentum is still conserved (as it always is in closed systems), but some kinetic energy is converted to heat, sound, or permanent deformation. This is what happens in most real-world collisions like car crashes.

Key difference: Elastic collisions conserve both momentum and energy. Inelastic collisions conserve momentum but lose kinetic energy.

Can momentum be negative?

Yes, absolutely. Since momentum is a vector quantity, it has both magnitude and direction. A negative momentum simply means the object is moving in the opposite direction to the positive reference direction you've chosen.

For example, if you define rightward motion as positive, then an object moving leftward would have negative momentum. The magnitude (absolute value) tells you how much momentum, while the sign tells you the direction.

Practical tip: In collision problems, use negative velocities for objects moving in opposite directions. This makes the math work out correctly for conservation of momentum.

Why do the collision results show m/s even when I input km/h?

The collision calculator converts all inputs to SI units (kilograms and meters per second) internally for accurate computation. This standardization ensures consistent and precise calculations regardless of which units you choose to input.

Final velocities are displayed in m/s as the standard output. However, the formula display shows your original input values with their units for reference, so you can verify the calculation matches your inputs.

Unit conversion: You can always convert the m/s results back to your preferred units. For example, multiply by 3.6 to convert m/s to km/h, or by 2.237 to convert to mph.

What does "momentum is conserved" mean?

Conservation of momentum means the total momentum of a closed system remains constant before and after a collision or interaction. This is one of the fundamental laws of physics and holds true for all types of collisions.

Mathematically: p₁ᵢ + p₂ᵢ = p₁f + p₂f

Where the subscript i means initial (before collision) and f means final (after collision).

The law of conservation of momentum states that for a collision occurring between object 1 and object 2 in an isolated system, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision.

— Newton's Third Law of Motion

This principle is why rockets work in space (expelling gas in one direction creates momentum in the opposite direction) and why recoil occurs when firing a gun.

How much energy is lost in a perfectly inelastic collision?

The energy loss depends on the masses and velocities of the objects involved. The calculator shows the exact kinetic energy before and after the collision, along with the percentage of energy lost.

This lost energy doesn't disappear — it's converted into other forms like:

  • Heat — Friction and deformation generate thermal energy
  • Sound — The collision produces sound waves
  • Deformation — Permanent changes to object shape
  • Vibration — Internal oscillations in the materials
Maximum energy loss: The maximum possible energy loss in a perfectly inelastic collision occurs when the objects have equal mass and opposite velocities. In this case, up to 50% of the kinetic energy can be lost.
Momentum
Formula
Momentum Comparison
Object 1
Negative = opposite direction
Object 2
Negative = opposite direction
Final Velocities
Formula
Momentum & Energy Analysis
About Momentum

Momentum is the product of mass and velocity. It is a vector quantity conserved in all collisions. In elastic collisions, both momentum and kinetic energy are conserved. In perfectly inelastic collisions, only momentum is conserved.

Type Formula
Linear Momentum p = mv
Elastic m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'
Perfectly Inelastic m₁v₁ + m₂v₂ = (m₁+m₂)v'
Switch between Linear Momentum and Collision tabs for different calculation modes
Select which variable to solve for by clicking the Momentum, Mass, or Velocity tabs
Use negative velocity in collision mode to represent objects moving in opposite directions
Click Unit Conversions to see your result in all available units
In elastic collisions, both momentum and kinetic energy are conserved
In perfectly inelastic collisions, objects stick together — some kinetic energy is lost
All calculations are performed locally in your browser
Want to learn more? Read documentation →
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