Momentum is a vector quantity; it has both magnitude and direction. Since momentum has a direction, it can be used to predict the resulting direction and speed of motion of objects after they collide. Mathematically represented as the product of an object’s mass and velocity.
p = mv
where p is momentum, m is mass, and v is velocity. Momentum is a vector quantity, meaning it has both magnitude and direction.
Conservation of Momentum Principle:
According to the conservation of momentum concept, if no outside forces act on an isolated system, its overall momentum stays constant. A system that has zero net external force is said to be isolated. The principle can be expressed mathematically as follows:
pinitial = pfinal
The system’s total momentum prior to an interaction is equal to its total momentum following the interaction.
Why Does Momentum Stay Conserved?
Newton’s third law of motion, which says, “For every action, there is an equal and opposite reaction,” directly leads to the conservation of momentum.
The force that one thing applies to the other during an interaction is equal to and opposite to the force that the other object applies. Although these forces alter their momenta, the system’s total momentum stays constant.
Applications of Conservation of Momentum
The principle of conservation of momentum is widely used in various scenarios, example:-
1.Collisions
Elastic Collisions: Objects bounce off each other without any loss of kinetic energy. Momentum is conserved.
Inelastic Collisions: Objects may stick together after collision, and kinetic energy is not conserved, but momentum is there.
2. Rocket Propulsion: In this, exhaust gases are ejected backwards by rockets to move forward. The rocket’s momentum in the opposite direction balances the momentum of the gases in one direction.
3. Recoil of Guns: The conservation of momentum causes the gun to move backward when a bullet is discharged. The gun’s backward momentum and the bullet’s forward momentum are equal.
Examples
1.Two Balls Colliding:
The total of the momenta of two balls prior to and after a collision in an isolated system is equal.
2. Stationary Objects:
The total momentum remains zero when a stationary item divides into two parts (for example, a firecracker exploding) because the momenta of the two portions in opposite directions balance out.
Importance in Physics
Momentum explain, how objects interact in the universe and it is the conservation of momentum. It determines how particles behave during interactions and is applicable to both mechanical systems and subatomic particles.
Note :-
Our knowledge of natural interactions is made simpler by the conservation of momentum. It aids in the explanation of anything from the dynamics of galaxies to the motion of common items. This concept emphasises how predictable and guaranteeing that a system’s total momentum stays constant in the absence of outside forces.
Key Points
When no external force acts on a system of several interacting particles , the total linear momentum of the system is conserved.
If F is external force acting on the system, then according to Newton’s second law, F = dp / dt. For an isolated system with no external force, i.e, F = 0 or dp / dt or p = constant or p1 + p2 ……+ pn = constant.
When a large force act for an extremely short duration neither the magnitude of the force nor the time for which it acts is important. In such case the total effect of force is measured. The effect of force is called impulse (measure of the action).
If a large force acts on a body or particle for a small time then, Impulse = product of force and time.
If a force F acts for a short time dt then impulse = Fdt.
If a force F acts for a finite interval of time from t1 and t2 then impulse = t1 sigma t2 Fdt
If a constant force acts for an interval triangle t then , impulse = F triangle t.
Impulse – Momentum : Impulse of a force is equal to the change in momentum F triangle = triangle p