Momentum Calculator

Calculate momentum, mass, or velocity using the momentum formula: p = m × v

What is Momentum?

Momentum is the quantity of motion possessed by a moving object. It depends on both how massive the object is and how fast it is moving. A truck moving slowly can have the same momentum as a bullet moving quickly.

Momentum Formula:

p = m × v

where: - p = momentum (measured in kg·m/s) - m = mass of the object (measured in kilograms) - v = velocity of the object (measured in m/s)

This formula can be rearranged to solve for any variable: - Mass: m = p / v - Velocity: v = p / m

How to Calculate Momentum

To find momentum, follow these steps:

1. Determine the mass: Measure or look up the object's mass (in kg, g, lb, etc.)

2. Determine the velocity: Measure how fast the object is moving and in what direction

3. Multiply mass by velocity: Use the formula p = m × v

4. Include units: Express your answer in appropriate units (kg·m/s, g·cm/s, etc.)

Example: A 1,500 kg car travels at 20 m/s. - p = 1,500 kg × 20 m/s = 30,000 kg·m/s

Conservation of Momentum

One of the most important principles in physics is the law of conservation of momentum: in a closed system with no external forces, the total momentum before an interaction equals the total momentum after.

m₁v₁ + m₂v₂ = m₁v₁' + m₂v₂'

This principle applies to: - Elastic collisions — objects bounce off each other (kinetic energy is conserved) - Inelastic collisions — objects deform or stick together (kinetic energy is not conserved) - Explosions — a single object breaks into pieces

Momentum vs. Impulse

Momentum is a property of a moving object at a given instant. Impulse is the change in momentum caused by a force acting over time:

J = F × Δt = Δp

This is why airbags work — they increase the time of impact, reducing the force even though the change in momentum (impulse) stays the same.

Types of Momentum

Linear Momentum: p = mv, the momentum of an object moving in a straight line. This is what the calculator above computes.

Angular Momentum: L = Iω, the rotational equivalent. It depends on the moment of inertia (I) and angular velocity (ω).

Real-World Applications of Momentum

• Vehicle safety: Designing crumple zones and airbags to manage momentum during crashes
• Sports: Understanding collisions in football, billiards, and baseball
• Rocket propulsion: Thrust is generated by conservation of momentum (expelling exhaust)
• Ballistics: Analyzing bullet impact and projectile behavior
• Particle physics: Tracking subatomic particle collisions in accelerators
• Astronomy: Calculating orbital mechanics and gravitational interactions

Common Questions About Momentum

What is the formula for momentum?

The momentum formula is p = m × v, where p is momentum, m is mass, and v is velocity. Momentum is a vector quantity measured in kg·m/s in SI units.

What is momentum in physics?

Momentum is the quantity of motion an object has. It depends on both mass and velocity — a heavier or faster object has more momentum. Momentum is conserved in collisions when no external forces act.

What is the law of conservation of momentum?

The law of conservation of momentum states that the total momentum of a closed system remains constant if no external forces act on it. In a collision, the total momentum before equals the total momentum after.

What is the difference between momentum and impulse?

Momentum (p = mv) is a property of a moving object, while impulse (J = F × t) is the change in momentum caused by a force over time. The impulse-momentum theorem states J = Δp.

Can momentum be negative?

Yes, momentum can be negative because it is a vector quantity. Negative momentum simply means the object is moving in the negative direction (opposite to the chosen positive direction).