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We all have seen momentum in our everyday life. A person walking on the street has a specific momentum- an electric motor rotating at a fast speed has a defined momentum. Each object or body which is in motion has a defined momentum. When we say, momentum is conserved it means that the momentum always remains the same before and after the motion or movement.
A ball has the same sum of stored energy and motion energy before throwing and after it is thrown. What changes then? The amount of stored energy and motion energy might change but the total mechanical energy remains unchanged. Stored energy is the potential energy while motion energy is the kinetic energy. The conservation of momentum, therefore, is the conservation of the total mechanical energy before and after the motion.
Conservation of momentum definition
Definition: A conservation of momentum occurs when the motion takes place in a closed system or a system with no friction or air resistance. When two bodies collide, the net momentum before the collision is equal to the net momentum after the collision.
Types of momentum
There are two types of momentum as described below.
Angular momentum: It is also called spin momentum because it is a property of objects that revolve, rotate, orbit, gyrate or spin. It is the rotational equivalent to linear momentum, the only difference is that the path of movement is in a circular orbit and not linear. Example: Earth revolving around the sun.
Linear momentum: In physics, linear momentum is defined as the product of the object’s mass and its velocity. An object that is travelling at a certain speed in a straight path has linear momentum. Example: Two balls colliding.
The centre of mass action
The centre of mass is a position that is defined relative to an object or body under study. The centre of mass acts as the entire mass in the closed system is concentrated in it. When a system of particles is under study, we don’t need to calculate the motion of every particle in the system but consider only the ideal point that corresponds to the system. This ideal point has motion that is the same as the motion of a particle in the system with a mass equal to the sum of the masses of all the particles in t1he system of particles considered earlier. It is the result of all the forces applied to all the particles in the system.
For two masses the centre of mass is → Xcm = (m1x1 + m2x2)/(m1 + m2)
Where Xcm→ distance to the centre of mass and m1x1 + m2x2 is the sum of momenta of individual masses.
Conservation of linear momentum
Momentum is the mass of an object times its velocity. When no external forces are present, an object’s linear momentum remains constant.
If a system of masses m1, m2, m 3 are moving with velocity v1, v2, v3 respectively, then
Total Linear momentum = m1v1 + m2v2 + m3v3…
Newton’s second law of motion explains that the external force applied is directly proportional to momentum change in a closed system.
Newton’s third law of motion is an action to reaction law because it explains that when two objects in a closed system collide, their magnitude is always equal and the direction of the force applied is in the opposite direction to each other.
Closed system definition: No friction, air resistance, or any external force present.
Derivation of conservation of linear momentum with the help of newton’s third and second law
In order to understand the conservation of momentum equation let’s consider two objects X and Y which have an initial velocity of u1 and u2 and after the collision, the velocity of both the objects changes to v1 and v2 respectively. Both the objects have mass of m1 and m2 respectively.
Δp1 = m1(v1– u1)
Δp1 = change in momentum for the first object
Δp2= m2(v2-u2)
Δp2 = change in momentum for the second object,
F1 = F2 – {1} (According to Newton’s third law of motion)
F1= force acting on object X due to object Y
F2= force acting on object Y due to object X
F1= m1a1 and
F2= m2a2 –{2} (According to Newton’s third law of motion)
m→ mass
a→ acceleration of the bodies
Therefore, substituting {2} in {1}, we obtain,
m1a1 = m2a2
m1(v1-u1) = m2(v2-u2) – (As a1 = (v1-u1)/t and a2=(v2-u2)/t)
m1u1 + m2u2 = m1v1 + m2v2 (Law of conservation of linear momentum)
Application of linear momentum
Rocket propulsion
1)Before the rocket is launched: The net momentum in the rocket is zero because it is in a state of rest. The rocket has zero velocity in this state, and hence mass multiplied by zero gives us zero momentum.
2)After the rocket is launched: The chemical energy in the form of fuel is burnt to transform into mechanical energy, which generates the force to propel the rocket. As the fuel reduces due to usage, the momentum increases because the rocket becomes lighter. Hence, the net momentum remains constant.
Conclusion
When we understand Newton’s laws of motion, the conservation of momentum principle is easy to comprehend. The law of conservation describes all the processes in which the energy is always conserved or remains unchanged overall in the motion. In the sections above, we defined the law of conservation of momentum, which says that momentum is also a quantity to which the law of conservation can be applied. The Law of conservation of momentum thus states that mass into velocity for an object or body in a closed system will always be constant. Momentum is always conserved in this closed system for every motion on earth.
