What Is Momentum?
Momentum is a vector quantity defined as the product of an object's mass and its velocity. In classical mechanics, it is represented by the symbol p and is measured in kilogram-meters per second (kg m/s). Momentum describes the quantity of motion an object possesses and plays a central role in Newton's laws of motion.
The concept of momentum is crucial because it is conserved in isolated systems. This conservation principle is one of the most powerful tools in physics, allowing us to predict the outcomes of collisions, explosions, and other interactions without knowing the details of the forces involved.
Momentum Formula
Where p is momentum (kg m/s), m is mass (kg), and v is velocity (m/s). Since velocity is a vector, momentum is also a vector quantity with both magnitude and direction.
Conservation of Momentum
| Collision Type | Momentum | Kinetic Energy |
|---|---|---|
| Elastic | Conserved | Conserved |
| Inelastic | Conserved | Not conserved |
| Perfectly Inelastic | Conserved | Maximum loss |
| Explosion | Conserved | Increases |
Example Calculations
- A 1,500 kg car traveling at 20 m/s has momentum of 30,000 kg m/s.
- A 0.145 kg baseball at 40 m/s has momentum of 5.8 kg m/s.
- A 100 kg sprinter at 10 m/s has momentum of 1,000 kg m/s.
Frequently Asked Questions
Can momentum be negative?
Yes. Since momentum is a vector, its sign depends on direction. In one-dimensional problems, we assign positive and negative directions, so an object moving in the negative direction has negative momentum.
What is the relationship between momentum and force?
Newton's second law states that force equals the rate of change of momentum: F = dp/dt. For constant mass, this simplifies to F = ma. The impulse (force times time) equals the change in momentum.
What is the de Broglie wavelength?
The de Broglie wavelength relates momentum to wave properties of matter: lambda = h/p, where h is Planck's constant. This relationship is fundamental to quantum mechanics and shows that all matter exhibits wave-like behavior.