Linear Momentum of a System of Particles
Understanding the total linear momentum of a system of particles and its relation to the velocity of the centre of mass.
What is Linear Momentum of a System of Particles?
A vector quantity defined as the product of an object's mass and its velocity.
Key formula / rule: Linear Momentum of a single particle
Key points
- Define and calculate the total linear momentum of a system of particles.
- Understand the relationship between the total linear momentum and the velocity of the center of mass.
- Apply the principle of conservation of linear momentum to solve problems.
- Differentiate between internal and external forces in a system.
Common exam trap
Confusing total momentum with the momentum of a single particle.
Definitions
- Term
Linear Momentum
- Meaning
A vector quantity defined as the product of an object's mass and its velocity.
- Term
System of Particles
- Meaning
A collection of discrete particles considered together as a single entity.
- Term
Center of Mass (CM)
- Meaning
A point representing the mean position of the matter in a body or system of bodies.
- Term
Conservation of Linear Momentum
- Meaning
The principle stating that the total linear momentum of an isolated system remains constant over time.
Learning objectives
Define and calculate the total linear momentum of a system of particles.
Understand the relationship between the total linear momentum and the velocity of the center of mass.
Apply the principle of conservation of linear momentum to solve problems.
Differentiate between internal and external forces in a system.
Formulae
- Name
Linear Momentum of a single particle
- Note
where 'm' is mass and 'v' is velocity.
- Expression
p = mv
- Name
Total Linear Momentum of a System of Particles
- Note
Vector sum of individual momenta.
- Expression
P = Σ pi = Σ (mi vi)
- Name
Relationship with Center of Mass Velocity
- Note
where M is the total mass of the system and Vc is the velocity of the center of mass.
- Expression
P = M Vc
- Name
Velocity of Center of Mass
- Note
where M = Σ mi is the total mass.
- Expression
Vc = (Σ mi vi) / M
Prerequisites
Definition of linear momentum for a single particle.
Vector addition.
Concept of center of mass.
Newton's laws of motion.
Common mistakes
Confusing total momentum with the momentum of a single particle.
Forgetting to treat momentum as a vector quantity, leading to errors in summation.
Assuming conservation of momentum when external forces are present.
Incorrectly calculating the velocity of the center of mass.
Keywords
Linear Momentum
System of Particles
Center of Mass
Conservation of Momentum
Vector Sum
External Force
Internal Force
Total Mass
Velocity of CM
Practice preview
A system of particles is initially at rest. If an internal force causes the particles to move, what can be said about the total linear momentum of the system?…
medium
What is the total linear momentum of a system of particles?…
easy
A system of particles is in motion. If no external force acts on the system, which of the following quantities remains conserved?…
medium