Impulse & Momentum
How forces change motion over time — and how momentum is conserved.
Impulse & Momentum – Motion Through Forces Acting Over Time
Quantify how forces change the state of motion of objects over time. Analyze collisions, explosions, and the fundamental principle of momentum conservation.
What is Momentum?
Momentum (p = mv) is the product of mass and velocity. It is a vector quantity — both magnitude and direction matter. A heavier, faster-moving object has more momentum and requires a greater impulse (force × time) to bring it to rest. Momentum is the reason a bullet can penetrate steel while a tennis ball bounces off.
What is Impulse?
Impulse (J = F·Δt) is the product of a force and the time interval over which it acts. By Newton's Second Law, impulse equals the change in momentum: J = Δp = m(v₂ - v₁). This impulse-momentum theorem is crucial in crash analysis, sports biomechanics, and rocket propulsion — situations where forces act for short, controlled durations.
Core Concepts You'll Learn Here:
- 📌 Linear Momentum (p = mv) – The 'quantity of motion' of an object.
- 📌 Impulse (J = F·Δt) – The effect of a force applied over a time interval.
- 📌 Impulse-Momentum Theorem – J = Δp; impulse equals change in momentum.
- 📌 Conservation of Momentum – In an isolated system, total momentum is constant.
- 📌 Perfectly Inelastic Collision – Objects stick together; maximum kinetic energy loss.
- 📌 Perfectly Elastic Collision – Both momentum and kinetic energy are conserved.
- 📌 Center of Mass Motion – The center of mass of an isolated system moves at constant velocity.
What You'll Find in This Section
This section provides three calculators: a Linear Momentum solver with three-way solving (p, m, or v), an Impulse calculator supporting both J = F·Δt and J = m·Δv approaches, and a Collision Analyzer that handles both perfectly inelastic and perfectly elastic two-body collisions with before/after momentum bar charts and kinetic energy comparison.
Impulse & Momentum Calculators
Momentum describes an object's quantity of motion. Impulse describes the effect of a force over time. Together they are fundamental to analyzing collisions, explosions, and any scenario where forces act for a finite duration.
Linear Momentum (p = mv): Solve for momentum, mass, or velocity. Understand how mass and speed contribute to an object's resistance to change in motion.
Impulse (J = F·Δt): Calculate the impulse from a constant force over a time interval, or from the change in momentum using initial and final velocities.
Collision Analyzer: Apply conservation of momentum to perfectly inelastic (objects merge) or perfectly elastic (kinetic energy conserved) collisions between two objects.
Linear Momentum Calculator
Momentum is the product of an object's mass and velocity. It is a vector quantity — direction matters. Use this calculator to solve for momentum, mass, or velocity.
Solve for:
Impulse Calculator (J = F · Δt)
Impulse is the product of a force and the time over which it acts. It equals the change in momentum of an object and describes how strongly a force affects the object's motion over time.
Change in Momentum (Δp = m·Δv)
Since impulse equals the change in momentum, we can also calculate impulse from the mass and the change in velocity. This approach is useful when force is unknown but initial and final velocities are given.
Collision Analyzer (Conservation of Momentum)
In any collision, the total linear momentum of an isolated system is conserved. Analyze perfectly inelastic collisions (objects stick together) or perfectly elastic collisions (kinetic energy also conserved).