Conservation of Momentum

A comprehensive tool for calculating linear and angular momentum in physics. Includes calculators for collision momentum, recoil velocity, and angular momentum conservation.

Conservation of Momentum

Linear Momentum

The momentum of a body is defined as the product of its mass and velocity:

ML = m × v

Where:

ML = linear momentum (kg·m/s)
m = mass of body (kg)
v = velocity of body (m/s)

Conservation Principle: The total linear momentum of a system before collision equals the total momentum after collision:

m₁v₁ + m₂v₂ + ... + mₙvₙ = m₁u₁ + m₂u₂ + ... + mₙuₙ

Angular Momentum

For a rotating body:

MR = ω × I

Where:

MR = angular momentum (kg·m²/s)
ω = angular velocity (rad/s)
I = moment of inertia (kg·m²)

Conservation of Angular Momentum: ω₁I₁ = ω₂I₂

Calculator

Inputs

Mass 1 (kg)

Velocity 1 (Before Collision) (m/s)

Mass 2 (kg)

Velocity 2 (Before Collision) (m/s)

Results

Total Momentum Before Collision-- kg·m/s

Combined Velocity (if stuck together)-- m/s

Calculator

Inputs

Projectile Weight (lb)

Projectile Velocity (Muzzle Speed) (ft/s)

Gun/Rifle Weight (lb)

Recoil Slow Down Distance (ft)

Results

Recoil Velocity-- ft/s

Recoil Kinetic Energy-- lb·ft

Recoil Force (to slow down)-- lb

Calculator

Inputs

Initial Rotation Velocity (rpm)

Initial Radius (m)

Final Radius (m)

Results

Final Rotation Velocity-- rpm