MOMENTUM
Momentum is a fundamental concept in physics that describes the motion of an object. Below is a breakdown of all key concepts related to momentum:
1. Linear Momentum
- Definition: Linear momentum is the product of an object’s mass and velocity.
- Formula: p=mv where:
- p: Momentum (vector quantity)
- m: Mass of the object (scalar quantity)
- v: Velocity of the object (vector quantity)
- SI Unit: kgm/s
2. Conservation of Momentum
- Principle: In an isolated system (no external forces), the total momentum remains constant.
- Formula: ∑pinitial = ∑pfinal
- Applications:
- Collisions (elastic and inelastic)
- Explosions
3. Impulse
- Definition: Impulse is the change in momentum caused by a force acting over a period of time.
- Formula: J=Δp=F⋅Δt where:
- J: Impulse
- Δp: Change in momentum
- F: Force applied
- Δt: Time duration
- SI Unit: Ns (Newton-second), which is equivalent to kgm/s.
4. Types of Collisions
- Elastic Collisions:
- Kinetic energy and momentum are conserved.
- Objects bounce off each other without deformation or heat generation.
- Inelastic Collisions:
- Momentum is conserved, but kinetic energy is not.
- Objects may stick together or deform after collision.
- Perfectly Inelastic Collision:
- A special case where objects stick together after collision.
5. Center of Mass and Momentum
- The momentum of a system of particles is the product of the total mass and the velocity of the center of mass: Ptotal=MVCM where:
- Ptotal: Total momentum of the system
- M: Total mass of the system
- VCM: Velocity of the center of mass
6. Angular Momentum
- Definition: Angular momentum is the rotational equivalent of linear momentum.
- Formula: L=r×p where:
- L: Angular momentum (vector)
- r: Position vector
- p: Linear momentum
- For a rotating rigid body: L= Iω where:
- I: Moment of inertia
- ω: Angular velocity
- Conservation of Angular Momentum:
- Linitial = Lfinal
7. Relativistic Momentum
- At speeds close to the speed of light, momentum is adjusted using the Lorentz factor:
- p= mv (1 – v2/c2)1/2 where:
- c: Speed of light in a vacuum (3×108 m/s)
- p= mv (1 – v2/c2)1/2 where:
8. Practical Examples of Momentum
- Sports (e.g., catching or hitting a ball)
- Vehicle collisions (analyzing crash dynamics)
- Rockets and propulsion (conservation of momentum in space)
- Conservation laws in particle physics.