Conservation of Momentum Definition, Theory
Conservation of momentum, states that the total momentum of an isolated system remains the same. The momentum which means motion remains unchanged in an isolated collection of objects. Momentum is the product of the mass of the object and the velocity at which it is travelling and is also equal to the total force required to bring the object to rest.
For any variety of a few articles, the complete energy is the entirety of the individual momenta. There is a quirk, notwithstanding, in that force is a vector, including both the heading and the size of the movement, so that the momenta of articles going in inverse ways can drop to yield a general aggregate of zero.
Prior to dispatch, the complete force of a rocket and its fuel is zero. During dispatch, the descending energy of the extending exhaust gases is just equivalent in size to the upward force of the rising rocket, with the goal that the complete force of the framework stays consistent—for this situation, at zero worth. In an impact of two particles, the whole of the two momenta before the crash is the same as their total after the crash. What force one molecule losses, different additions.
The law of conservation of momentum is confirmed both experimentally and can also be proved mathematically, under a reasonable presumption that space is uniform. The law of momentum exists in nature and the statement is just a theoretical statement that states the observations made during the experiments.
There is a comparative preservation law for precise force, which portrays rotational movement is basically a similar manner that conventional energy depicts straight movement. Despite the fact that the exact numerical articulation of this law is fairly more included, instances of it are various. All helicopters, for example, need at any rate two propellers (rotors) for adjustment. The body of a helicopter would turn the other way to moderate precise force if there were just a solitary flat propeller on top. As per preservation of Angular momentum conservation, ice skaters turn quicker as they pull their arms toward their body and all the more gradually as they expand them
Angular momentum conservation has likewise been completely settled by analysis and can be appeared to follow numerically from the sensible assumption that space is uniform concerning direction—that will be, that there isn't anything in the laws of nature that singles out one heading in space as being exceptional contrasted and some other. For at least two bodies in a separate framework following up on one another, their complete energy stays steady except if an outer power is applied. Hence, energy cannot be made nor pulverized.
The Logic Behind the Law
Think about a crash between two things - objects 1 and 2. For such a crash, the powers acting between the two items are similar in size and inverse in the heading (Newton's third law). This statement can be communicated in condition structure as follows.
F1= -F2
The powers demonstration between the two articles for a given measure of time. At times, the time is long; in different cases the time is short. Notwithstanding how long the time is, it very well may be said that the time that the power follows up on object 1 is equivalent to the time that the power follows up on object 2. This is simply coherent. Powers result from connections (or contact) between two items. In the event that object 1 contacts object 2 for 0.050 seconds, at that point object 2 must contact object 1 for a similar measure of time (0.050 seconds). As a condition, this can be expressed as
T1= T2
Since the powers between the two articles are equivalent in extent and inverse in course, and since the occasions for which these powers demonstrate are equivalent in greatness, it follows that the motivations experienced by the two items are additionally equivalent in size and inverse in bearing. As a condition, this can be expressed as
F1*T1= -F2*T2
Yet, the drive experienced by an article is equivalent to the adjustment in the energy of that object (the motivation force change hypothesis). Hence, since each article encounters equivalent and inverse driving forces, it follows legitimately that they should likewise encounter equivalent and inverse energy changes. As a condition, this can be expressed as
M1*ΔV1= M2*ΔV2
FAQs on Conservation of Momentum
1. What is the law of conservation of momentum as per the CBSE Class 11 syllabus for 2025-26?
The law of conservation of momentum states that for an isolated system, the total momentum remains constant. This means that if there is no net external force acting on a system of interacting objects, the vector sum of their momenta will be the same before, during, and after any interaction. Momentum, a vector quantity, is the product of an object's mass and its velocity (p = mv).
2. What is the formula used to apply the principle of conservation of momentum in a collision?
For a simple collision between two objects in an isolated system, the formula for conservation of momentum is: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂. In this equation:
- m₁ and m₂ are the masses of the first and second objects, respectively.
- u₁ and u₂ are their initial velocities before the collision.
- v₁ and v₂ are their final velocities after the collision.
3. How is the law of conservation of momentum related to Newton's Laws of Motion?
The law of conservation of momentum is a direct consequence of Newton's Third Law of Motion. During a collision, the force exerted by the first object on the second (action) is equal in magnitude and opposite in direction to the force exerted by the second object on the first (reaction). Since these forces act for the same amount of time, the impulses (Force × time) are equal and opposite. As impulse equals the change in momentum, the momentum change for one object is exactly equal and opposite to the momentum change of the other, meaning the total momentum of the system remains unchanged.
4. What are some real-world examples that demonstrate the conservation of momentum?
The principle of conservation of momentum can be observed in many everyday scenarios. Some key examples include:
- Recoil of a Gun: When a bullet is fired, it moves forward with high momentum. To conserve the total momentum (which was initially zero), the gun recoils backward with equal and opposite momentum.
- Rocket Propulsion: A rocket expels hot gases downward at high velocity. To conserve momentum, the rocket itself is propelled upward.
- Billiard Ball Collisions: In a game of billiards, the total momentum of all the balls just before a collision is equal to the total momentum of all the balls just after the collision.
- An Astronaut in Space: If an astronaut floating in space throws a tool, the astronaut will move in the opposite direction to conserve the system's overall momentum.
5. What is the difference between conservation of momentum and conservation of kinetic energy?
While both are conservation laws, they apply under different conditions. The key difference is that momentum is conserved in all isolated collisions (both elastic and inelastic), whereas kinetic energy is conserved only in elastic collisions. In an inelastic collision, some kinetic energy is converted into other forms like heat, sound, or deformation, but the total momentum of the system is still conserved.
6. How does an external force like gravity affect the conservation of momentum?
The law of conservation of momentum strictly applies only to an isolated system, which means a system with no net external force. Gravity is an external force. Therefore, if your system consists only of two colliding balls in mid-air, their momentum is not conserved in the vertical direction because of gravity. However, if you define the system to include the balls and the Earth, gravity becomes an internal force, and the total momentum of the ball-Earth system is conserved.
7. What conditions are necessary for the law of conservation of momentum to be valid?
The single most important condition for the law of conservation of momentum to apply is that the system must be isolated. This means that the net external force acting on the system of objects must be zero. The law accounts for internal forces, such as the forces between colliding particles, but any force originating from outside the system (like friction or air resistance) will change the system's total momentum.
