The total momentum of a system of masses (i.e. moving bodies) in any one direction remains constant, unless acted upon by an external force in that direction. This statement is called-
Principle of conservation of momentum
Understanding the Principle of Conservation of Momentum
The question describes a fundamental concept in physics related to the motion of a system of bodies. It states that the total momentum of a system remains constant in a particular direction unless an external force acts on the system in that direction.
Let's break down the key terms:
- System of masses: This refers to a group of objects that we are considering together.
- Momentum: Momentum is a measure of the mass in motion. For a single object, it is calculated as the product of its mass ($\(m\)$) and its velocity ($\(v\)$). Mathematically, momentum $\(p = mv\)$. Momentum is a vector quantity, meaning it has both magnitude and direction.
- Total momentum of a system: This is the vector sum of the individual momenta of all the objects within the system.
- External force: This is a force acting on the system from outside the system. Forces exerted by objects within the system on each other are called internal forces.
- Remains constant: This means the total momentum before an interaction (like a collision or explosion) is equal to the total momentum after the interaction, provided there are no external forces.
The statement perfectly describes the Principle of Conservation of Momentum.
In simpler terms, if you have a group of objects that are only interacting with each other (like colliding), their total momentum stays the same in any specific direction, as long as no force from outside the group is pushing or pulling on them in that direction.
Principle of Conservation of Momentum Explained
The principle of conservation of momentum is a direct consequence of Newton's third law of motion. When two objects interact, the force object A exerts on object B is equal in magnitude and opposite in direction to the force object B exerts on object A. These internal forces cause changes in the individual momenta of the objects, but the total momentum of the system remains unchanged if there are no external forces.
Consider a system of two particles with masses \(m_1\) and \(m_2\) and initial velocities \(u_1\) and \(u_2\). If they interact and their final velocities are \(v_1\) and \(v_2\), the principle states:
Total initial momentum = Total final momentum
\[ \(m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2\) \]
This principle is particularly useful for analyzing collisions and explosions where internal forces are dominant and external forces (like friction or air resistance) can be neglected or are zero.
Analyzing the Options
Let's look at why the other options are incorrect:
- Principle of conservation of energy: This principle states that the total energy of an isolated system remains constant, although energy can be transformed from one form to another (like kinetic energy to potential energy or heat). While often related to momentum conservation, it's a different concept dealing with energy, not momentum.
- Newton's first law of motion: This law states that an object will remain at rest or in uniform motion in a straight line unless acted upon by a net external force. This applies to a single body and describes its state of motion, not the conservation of total momentum for a system.
- Law of transmissibility of forces: This law applies to rigid bodies and states that a force acting on a rigid body can be considered to act at any point along its line of action without changing the external effect on the body. This principle is used in statics and the analysis of forces on rigid bodies, not the conservation of momentum for a system of moving masses.
Based on the definition provided in the question, the correct statement is the Principle of Conservation of Momentum.
Revision Table: Comparing Related Physics Principles
| Principle/Law | Key Concept | Applies To |
|---|---|---|
| Conservation of Momentum | Total momentum of a system remains constant if no net external force acts on it. | System of masses (moving bodies) |
| Conservation of Energy | Total energy of an isolated system remains constant. | System of objects/energy transformations |
| Newton's First Law | An object's state of motion (rest or uniform velocity) changes only if a net external force acts. | Single body |
| Law of Transmissibility of Forces | External effect of a force on a rigid body is independent of the point of application along its line of action. | Rigid bodies (statics/external effects) |
Additional Information on Momentum Conservation
The principle of conservation of momentum is a very powerful tool in physics, especially when analyzing collisions and explosions because internal forces are often much larger than external forces during these short events, allowing external forces to be ignored as a first approximation.
- In an elastic collision, both momentum and kinetic energy are conserved.
- In an inelastic collision, momentum is conserved, but kinetic energy is not (some is lost as heat or sound).
- Even in seemingly complex scenarios like rocket propulsion, the principle of momentum conservation is applied (the momentum gained by the expelled propellant is equal and opposite to the momentum gained by the rocket).
Understanding this principle is crucial for solving many problems involving interacting bodies.
Important Questions from Conservation of Linear Momentum
- A particle of mass $6m$ at rest suddenly breaks on its own into three fragments.
Two fragments of mass $m$ and $2m$ move along mutually perpendicular directions with speeds $2v$ and $v$ respectively.
The energy released during the process is, - Body A of mass $m$ moving with speed $u$ collides with another body B of mass $3m$, at rest. The collision is head-on and elastic in nature. After the collision, the fraction of energy lost by the colliding body A is:
What are the dimensions of angular momentum?
The propulsion of a rocket is based on which of Newton's laws of motion?
For a system of interacting particles, which condition is fundamental for the conservation of its total linear momentum $\vec{P}$?
