Momentum
Momentum is the product of an object's mass and its velocity, representing the quantity of motion possessed by the object. It is a vector quantity, meaning it has both magnitude and direction aligned with the velocity. Momentum is fundamental to Newton's second and third laws and is the conserved quantity in isolated systems during collisions and interactions.
Key Formula
p = m × v
LaTeX: p = m \cdot v
| Symbol | Meaning | Unit |
|---|---|---|
| p | Linear momentum | kg·m/s or N·s |
| m | Mass of the object | Kilogram (kg) |
| v | Velocity of the object | Metre per second (m/s) |
Worked Example
Problem
A truck of mass 4,000 kg travels at 15 m/s east. A car of mass 800 kg travels at 25 m/s east. Which has greater momentum and by how much?
Solution
Step 1: Calculate momentum of the truck. p_truck = m × v = 4,000 × 15 = 60,000 kg·m/s (east) Step 2: Calculate momentum of the car. p_car = m × v = 800 × 25 = 20,000 kg·m/s (east) Step 3: Compare. Difference = 60,000 - 20,000 = 40,000 kg·m/s
Answer
Truck momentum = 60,000 kg·m/s; Car momentum = 20,000 kg·m/s; Truck has 40,000 kg·m/s more momentum.
Momentum of Common Moving Objects
| Object | Mass (kg) | Speed (m/s) | Momentum (kg·m/s) |
|---|---|---|---|
| Bullet (pistol) | 0.01 | 400 | 4 |
| Cricket ball (bowled) | 0.16 | 40 | 6.4 |
| Cyclist | 80 | 10 | 800 |
| Car | 1,200 | 30 | 36,000 |
| Train | 500,000 | 50 | 25,000,000 |
| Aircraft (takeoff) | 300,000 | 80 | 24,000,000 |
Interactive Tools
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Related Terms
Impulse
Impulse is the product of a force and the time interval over which it acts, and it equals the change in momentum of the object. It is a vector quantity that describes the total effect of a force applied over time rather than instantaneously. Impulse is widely used in collision analysis, sports biomechanics, and safety engineering to understand how forces affect motion.
Conservation of Momentum
The law of conservation of momentum states that the total momentum of a closed, isolated system remains constant if no external net force acts on it. This means the sum of momenta of all objects before an interaction equals the sum after the interaction. It is one of the most fundamental conservation laws in physics and applies equally to collisions, explosions, and all mechanical interactions.
Elastic Collision
An elastic collision is one in which both the total kinetic energy and the total momentum of the system are conserved before and after the collision. No energy is lost to deformation, heat, or sound, making it an idealized model most closely approximated by atomic and subatomic particle interactions. Billiard ball collisions and gas molecule interactions are common approximations of elastic collisions.
From Latin "momentum" meaning "movement" or "moment", derived from "movere" (to move). The concept was mathematically formalized by René Descartes in the 17th century and later refined by Isaac Newton.