Principle of Conservation of Linear Momentum
Statement and applications of the law of conservation of linear momentum in isolated systems.
What is Principle of Conservation of Linear Momentum?
A vector quantity defined as the product of an object's mass and its velocity (p = mv). It measures the 'quantity of motion' an object possesses.
Key formula / rule: Linear Momentum
Key points
- State the principle of conservation of linear momentum.
- Explain the conditions under which linear momentum is conserved.
- Apply the principle to solve problems involving collisions and explosions.
- Relate the conservation of linear momentum to Newton's third law.
Common exam trap
Assuming momentum is conserved when external forces are significant.
Definitions
- Term
Linear Momentum
- Meaning
A vector quantity defined as the product of an object's mass and its velocity (p = mv). It measures the 'quantity of motion' an object possesses.
- Term
Isolated System
- Meaning
A system on which no net external force acts. In reality, systems are often approximated as isolated if external forces are very small compared to internal forces.
- Term
Collision
- Meaning
An event in which two or more bodies exert forces on each other for a relatively short time. Momentum is conserved if the system is isolated.
- Term
Elastic Collision
- Meaning
A collision in which both momentum and kinetic energy are conserved.
- Term
Inelastic Collision
- Meaning
A collision in which momentum is conserved, but kinetic energy is not. Some kinetic energy is lost as heat, sound, or deformation.
Learning objectives
State the principle of conservation of linear momentum.
Explain the conditions under which linear momentum is conserved.
Apply the principle to solve problems involving collisions and explosions.
Relate the conservation of linear momentum to Newton's third law.
Differentiate between conserved and non-conserved quantities in a system.
Formulae
- Name
Linear Momentum
- Note
Momentum is the product of mass and velocity. It is a vector quantity.
- Expression
p = mv
- Name
Conservation of Linear Momentum
- Note
Total momentum of an isolated system before an event equals the total momentum after the event.
- Expression
Pinitial = Pfinal
- Name
Collision of two bodies
- Note
Applies to systems where external forces are negligible during the collision.
- Expression
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
- Name
Explosion of a body at rest
- Note
The sum of momenta of fragments after explosion equals zero if the body was initially at rest.
- Expression
0 = m₁v₁ + m₂v₂ + ...
Prerequisites
Newton's Laws of Motion (especially the third law)
Concept of Force
Concept of Momentum (p = mv)
Vector Addition
Common mistakes
Assuming momentum is conserved when external forces are significant.
Treating momentum as a scalar quantity instead of a vector.
Confusing conservation of momentum with conservation of kinetic energy.
Incorrectly applying the principle to non-isolated systems.
Keywords
Linear Momentum
Conservation Law
Isolated System
Newton's Third Law
Collisions
Explosions
Vector Quantity
Impulse
Practice preview
Two billiard balls of equal mass are moving at right angles to each other with speeds v1 and v2. After collision, they move with speeds v3 and v4 respectively. If the collision is elastic, which of the following is true?…
medium
Which of the following statements correctly describes the principle of conservation of linear momentum?…
easy
A system consists of two particles of masses m1 and m2, moving with velocities v1 and v2 respectively. If the system is isolated, which of the following is true about the total momentum?…
easy