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Momentum

Momentum p = mv: quantity of motion. Conserved in closed systems. Impulse J = FΔt equals change in momentum. Elastic collisions conserve KE; inelastic lose KE to heat and deformation.

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p = mv; vector quantity with direction J = FΔt = Δp (impulse-momentum theorem) Elastic: KE conserved; inelastic: KE lost Coefficient e = (v₂′-v₁′)/(v₁-v₂)

Key quantities
p = mv
Momentum
Key relation
J = FΔt
Impulse
Key relation
Σp = const
Conservation
Key relation
kg·m/s
Unit
Key relation

Ready to run the numbers?

Why: Momentum conservation predicts collision outcomes. Impulse explains how force over time changes motion. Essential for ballistics, vehicle safety, and sports physics.

How: p = mv for single object. For collisions: Σp_before = Σp_after. Elastic: use 1D formulas for v₁′, v₂′. Inelastic: common final velocity v′ = Σp/Σm.

p = mv; vector quantity with directionJ = FΔt = Δp (impulse-momentum theorem)
Sources:Physics Classroom - MomentumHyperPhysics - Momentum

Run the calculator when you are ready.

Calculate MomentumEnter mass, velocity, or force and time

📚 Real-World Momentum Scenarios

Select a pre-configured example to explore momentum and collision physics:

For educational and informational purposes only. Verify with a qualified professional.

🔬 Physics Facts

🎱

Billiard balls demonstrate near-perfect elastic collisions

— Physics Classroom

💥

Car crashes are inelastic; KE converts to sound, heat, deformation

— HyperPhysics

🚀

Rocket propulsion uses conservation of momentum

— MIT OCW

⚾

Bat hitting ball applies impulse, changing momentum in milliseconds

— Khan Academy

⚙️ Momentum Parameters

Calculation Mode

Object 1 Properties

Mass of object 1
Velocity before collision/impulse
For impulse calculations

Unit Settings

momentum@bloomberg:~$
MOMENTUM: LOW
TOTAL MOMENTUM
50.00 kg·m/s
MOMENTUM 1
50.00 kg·m/s
KINETIC ENERGY
125.00 J
COLLISION TYPE
N/A

📊 Momentum Analysis Results

Object 1 Momentum
50.00
kg·m/s
Total Momentum
50.00
kg·m/s (conserved)
Kinetic Energy
125.00
Joules (before)
Energy Lost
0.0%
N/A
Final Velocity 1
5.00 m/s
Final Velocity 2
0.00 m/s
KE After
125.00 J
Conservation
Momentum Conserved

📈 Momentum Analysis Dashboard

🎱 Momentum Comparison

Before and after momentum analysis

⚡ Energy Distribution

Kinetic energy conservation analysis

🚀 Velocity Changes

Before and after velocities

🎯 Collision Elasticity

Coefficient of restitution (e)

📝 Step-by-Step Solution

📊 Input Parameters

Calculation Mode: BASIC MOMENTUM

🧮 Momentum Calculations

Using momentum formula: p = m × v

p = 10.00 kg × 5.00 m/s

→ p = 50.0000 kg·m/s

Kinetic Energy: KE = ½mv²

KE = 0.5 × 10.00 × (5.00)²

→ KE = 125.0000 J

⚡ Energy Analysis

Kinetic Energy Before:

→ KE_before = 125.0000 J

Kinetic Energy After:

→ KE_after = 125.0000 J

🌍 Momentum Reference Guide

ObjectMomentum (kg·m/s)Comparison
🚶Walking Person (70kg)98.02.0x less
🏃Sprinting Athlete700.014.0x less
🚴Bicycle + Rider400.08.0x less
🚗Car at 60 km/h25000.0500.0x less
🔫Bullet (9mm)4.810.4x more
⚾Baseball Pitch6.57.7x more
🚂Freight Train5.0e+71.0e+6x less
✈️Commercial Jet2.0e+7400000.0x less

📋 Key Takeaways

  • • Momentum (p = mv) is a vector quantity representing the quantity of motion
  • • Conservation of momentum applies to all collisions in closed systems
  • • Impulse (J = FΔt) equals the change in momentum
  • • Elastic collisions conserve both momentum and kinetic energy
  • • Inelastic collisions conserve momentum but lose kinetic energy

💡 Did You Know?

🎱Billiard balls demonstrate near-perfect elastic collisions, conserving both momentum and kinetic energySource: Physics Classroom
🚗Car crashes are inelastic collisions - kinetic energy is converted to sound, heat, and deformationSource: HyperPhysics
🚀Rocket propulsion uses conservation of momentum - ejecting fuel backward propels the rocket forwardSource: MIT OCW
⚾A baseball bat hitting a ball applies impulse, changing the ball's momentum dramatically in millisecondsSource: Khan Academy
💥Explosions conserve momentum - fragments fly apart but total momentum remains zeroSource: University Physics
🎯Newton's cradle demonstrates perfect momentum transfer through elastic collisionsSource: Physics Classroom

📖 What is Momentum?

Momentum is a fundamental concept in physics representing the "quantity of motion" an object possesses. It's defined as the product of an object's mass and velocity, making it a vector quantity with both magnitude and direction.

🎱 Key Properties

  • • Symbol: p (lowercase)
  • • Formula: p = mv
  • • SI Unit: kg·m/s or N·s
  • • Type: Vector (has direction)

⚡ Conservation Law

  • • Total momentum in closed systems is conserved
  • • Applies to all collision types
  • • Fundamental law of nature
  • • Valid in classical and quantum mechanics

Unlike energy, momentum is always conserved in collisions (assuming no external forces). This makes it incredibly useful for analyzing impacts, explosions, and rocket propulsion.

🧮 How to Calculate Momentum

Basic Momentum

p = m × v

Example: A 10 kg object moving at 5 m/s
p = 10 × 5 = 50 kg·m/s

Impulse-Momentum Theorem

J = F × Δt = Δp

Impulse equals the change in momentum and can be calculated from force and time.

Collision Equations

Conservation:

m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'

Elastic (1D):

v₁' = ((m₁-m₂)v₁ + 2m₂v₂)/(m₁+m₂)

Perfectly Inelastic:

v' = (m₁v₁ + m₂v₂)/(m₁ + m₂)

Coefficient of Restitution:

e = (v₂' - v₁')/(v₁ - v₂)

💥 Types of Collisions

Elastic Collision

e = 1 (perfect bounce)

  • • Both momentum AND energy conserved
  • • Objects bounce apart
  • • Example: Billiard balls, atomic collisions
  • • No energy lost to heat/sound

Inelastic Collision

0 < e < 1

  • • Momentum conserved, energy NOT
  • • Some energy lost to deformation
  • • Example: Car crashes, most real collisions
  • • Objects may separate or stick

Perfectly Inelastic

e = 0 (objects stick)

  • • Maximum kinetic energy loss
  • • Objects stick together after impact
  • • Example: Bullet lodging in target
  • • Common velocity after collision

📐 Momentum Formulas Reference

FormulaVariablesDescription
p = mvm = mass, v = velocityBasic momentum definition
J = FΔtF = force, Δt = time intervalImpulse from force
J = Δp = mΔvΔp = change in momentumImpulse-momentum theorem
Σp_before = Σp_afterClosed systemConservation of momentum
KE = ½mv²m = mass, v = velocityKinetic energy for comparison

🔗 Related Calculators

🚀Velocity Calculator

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💥Impulse Calculator

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⚖️Conservation of Momentum

Analyze momentum conservation

⚡Kinetic Energy

Calculate kinetic energy

💪Force Calculator

Calculate force (F = ma)

🍎Free Fall Calculator

Analyze free fall motion

❓ Frequently Asked Questions

What is momentum and how is it conserved?

Momentum (p = mv) is the product of mass and velocity, a vector quantity. Conservation of momentum states that in a closed system with no external forces, total momentum before equals total momentum after: Σp_before = Σp_after. This fundamental principle applies to all collisions and interactions.

What is the difference between elastic and inelastic collisions?

Elastic collisions conserve both momentum and kinetic energy - objects bounce apart. Inelastic collisions conserve momentum but lose kinetic energy - objects stick together or deform. Perfectly inelastic collisions have maximum energy loss, with objects moving together after collision.

How do I calculate impulse?

Impulse (J) equals the change in momentum: J = Δp = FΔt, where F is average force and Δt is time interval. Impulse can also be calculated as J = mΔv. Impulse-momentum theorem states that impulse equals the change in momentum, useful for analyzing collisions and impacts.

What is the coefficient of restitution?

Coefficient of restitution (e) measures collision elasticity: e = (v₂' - v₁')/(v₁ - v₂), where primes indicate final velocities. e = 1 for perfectly elastic collisions, e = 0 for perfectly inelastic collisions. Values between 0 and 1 represent partially elastic collisions.

How does momentum relate to force?

Force equals the rate of change of momentum: F = dp/dt = d(mv)/dt. For constant mass, F = ma. Impulse (FΔt) equals change in momentum. This relationship connects Newton's laws to momentum conservation and is fundamental to understanding collisions and motion.

Can momentum be negative?

Yes! Momentum is a vector quantity, so it has direction. Negative momentum simply means motion in the opposite direction from the positive reference direction. In one-dimensional problems, negative values indicate motion in the negative direction. The magnitude is always positive.

What does "HIGH", "MODERATE", and "LOW" mean in the Bloomberg Terminal risk indicator?

The Bloomberg Terminal risk indicator categorizes momentum levels: "HIGH" (p > 10,000 kg·m/s) indicates very high momentum requiring significant safety measures, typical of vehicles, projectiles, or large moving objects. "MODERATE" (100 < p ≤ 10,000 kg·m/s) represents typical momentum for sports, machinery, or medium objects. "LOW" (p ≤ 100 kg·m/s) indicates small momentum for everyday objects or low-speed interactions.

How do I analyze two-dimensional collisions?

For 2D collisions, resolve momentum into x and y components. Conservation applies separately: Σp_x,before = Σp_x,after and Σp_y,before = Σp_y,after. Use vector addition for total momentum. Requires solving simultaneous equations for final velocities in both directions.

📚 Official Data Sources

Physics Classroom - Momentum

Comprehensive momentum tutorials and examples

HyperPhysics - Momentum

Momentum concepts and formulas

Khan Academy - Linear Momentum

Momentum conservation and impulse

MIT OpenCourseWare - Classical Mechanics

University-level physics courses

University Physics (Young & Freedman)

Standard university physics textbook

⚠️ Disclaimer

This calculator is for educational and physics analysis purposes. Momentum calculations assume idealized conditions and may vary in real-world collisions. Actual collisions involve friction, deformation, heat generation, and other energy losses not accounted for in simplified models. Coefficient of restitution varies with impact speed and material properties. For safety-critical applications (automotive safety, sports equipment, impact analysis), consult professional engineers and conduct physical testing. Always use appropriate safety margins.

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