application

1. MOMENTUM BY: MISS RITIMA
Momentum can be defined as "mass in motion." All objects have mass; so if an object is moving, then
it has momentum - it has its mass in motion.
Momentum depends upon two variables mass and velocity.
In terms of an equation, the momentum of an object is equal to the mass of the object times the
velocity of the There are two kinds of momentum:
a. Linear momentum - An object travelling with velocity has linear momentum (mv).
b. Angular momentum -A spinning object has angular momentum.
Linear momentum
Linear momentum of a body is product of mass of body and velocity of body.
P =mv
Linear momentum of a body at rest is zero.
It is a vector quantity.
SI unit of momentum is kgm/s.
Angular momentum
Angular momentum is the quantity of rotation of a body, which is the product of its moment of inertia
and its angular velocity.
Angular momentum is a vector quantity that represents the product of a body's rotational inertia and
rotational velocity about a particular axis.
SI units for angular momentum are kg-m2
/sec.
Law of conservation of momentum
“In an isolated system (no external force), the algebraic some of the momenta of bodies, along any
straight line, remains constant and is not changed due to their mutual action and reaction on each
other”.
Consider a body ‘A’ of mass ‘m1’ moving with a velocity strike against another body ‘B’ of mass
m2,moving with velocity in same direction as shown in the below figure. Two bodies remain in contact
with each other for small time‘t’. They get separated and move with velocities and after collision.
Let be the force exerted by ‘A’ upon ‘B’ and be its reaction. Since the system is
isolated, i.e., no external force is there,
So,
…... (1)
This is in accordance with Newton’s third law of motion that ‘action and reaction are equal and
opposite.’
Substituting for and in equation (1),
Or,

2. Thus, the total momentum of the system before collision is equal to the total momentum of the system
after collision.
This verifies the law of conservation of momentum.
It may be noted that the conservation of momentum is closely connected with the validity of Newton’s
third law of motion, since we have used equation (1) [which is nothing but third law] to prove it.
Considering the momenta of the bodies before and after collision.
APPLICATION OF CONSERVATION OF MOMENTUM
(a) Recoil of Gun
A gun and a bullet constitute one isolated system. On firing the gun, bullet moves out with a very high
velocity . The gun experiences a recoil. It moves in the opposite direction as shown in the below
figure. Velocity ‘ ’ of the recoil gun can be calculated by the application of law of conservation of
momentum.
Before Firing After Firing
Momentum of bullet = 0 Momentum of bullet =
Momentum of gun = 0 Momentum of gun =
Total momentum of the system = 0 Total momentum of the system =

3. Here ‘m’ and ‘M’ are the masses of bullet and gun respectively. According to the law of conservation of
momentum, momentum before collision and after collision must be same.
or,
or,
Negative sign indicates that direction of motion of gun is in opposite direction.
(b) Rocket and Jet Plane
Fuel and oxygen is burnt in the ignition chamber. As hot gases escape from a rear opening, with some
momentum, the rocket moves in the forward direction with the same momentum.
(c) Explosion of a Bomb
Momentum of a bomb before explosion is zero. After explosion different fragments fly in various
directions. It will be observed that their momenta, when represented by the slide of a polygon, from a
closed polygon, indicating that net momentum after explosion is also zero. Thus, if the bomb exploded
into two fragments, they must move in opposite directions.
(d) A man Jumping from a Boat
When a man jumps from the boat to the shore, the boat is pushed backward. It can, exactly, be explained as in the
case of recoil of gun.