basic idea on momentum with a couple of interesting numerical ........ download to enjoy the effects

3. Conservation of linear momentum
The law of conservation of linear momentum is a fundamental law of nature, and it
states that if no external force acts on a closed system of objects, the momentum
of the closed system remains constant. One of the consequences of this is that the
center of mass of any system of objects will always continue with the same
velocity unless acted on by a force from outside the system. Conservation of
momentum is a mathematical consequence of the homogeneity (shift symmetry ) of
space (position in space is the canonical conjugate quantity to momentum). So,
momentum conservation can be philosophically stated as "nothing depends on location
per se".
Kinetic energy, on the other hand, is not conserved in collisions if they are
inelastic. Since momentum is conserved it can be used to calculate an unknown
velocity following a collision or a separation if all the other masses and velocities
are known.
A common problem in physics that requires the use of this fact is the collision of
two particles. Since momentum is always conserved, the sum of the momenta
before the collision must equal the sum of the momenta after the collision:
where u1 and u2 are the velocities before collision, and v1 and v2 are the velocities
after collision.

4. Angular Momentum
Objects executing motion around a point possess a quantity
called angular momentum. This is an important physical quantity
because all experimental evidence indicates that angular momentum
is rigorously conserved in our Universe: it can be transferred, but it
cannot be created or destroyed. For the simple case of a small mass
executing uniform circular motion around a much larger mass (so that
we can neglect the effect of the center of mass) the amount of angular
momentum takes a simple form. As the adjacent figure illustrates the
magnitude of the angular momentum in this case is L = mvr, where L is
the angular momentum, m is the mass of the small object, v is the
magnitude of its velocity, and r is the separation between the objects.

6. 1. Consider an example -when there happens a collision between moving
train & bus , then nothing happens to train and bus gets totally crushed , why?
Also, when train halts at the station, then it takes some time to do that.
But it is not true for bus . Why?
This is because of high mass of train.
Thus, by seeing above examples we can say that heavier bodies (like train)
takes some time to bring it's velocity to zero when brakes are applied though
train and bus are moving with the same velocity. Therefore,to describe the
motion of body , not only velocity is considered but mass is also taken into
account.
The total quantity of motion possessed by a moving body is known as the
momentum of the body. It has both magnitude and direction and hence a vector
quantity.it is denoted by p.
magnitude of p=mv
Where m is mass of body
v is velocity of body

7. 2.Example-when the bullet is fired , it moves in the forward direction and
the gun kicks backward. It is because before firing total momentum of system
constituted of barrel and gun is zero. When bullet is fired it gains some
momentum(due to velocity acquired by it) but to nullify this momentum gain, gun
moves in backward direction such that it has momentum equal in magnitude to
momentum of bullet with opposite direction.
Where m is mass of body and v is velocity of body
Law
In the absence of external forces , the total momentum of the body is
conserved.
Example-when the bullet is fired , it moves in the forward direction and the
gun kicks backward. It is because before firing total momentum of system
constituted of barrel and gun is zero. When bullet is fired it gains some
momentum(due to velocity acquired by it) but to nullify this momentum gain, gun
moves in backward direction such that it has momentum equal in magnitude to
momentum of bullet with opposite direction.

8. Rocket Propulsion
The motion of a rocket is an application of Newton's third law of motion and law of
conservation of linear momentum.
A rocket is a projectile that carries the rocket fuel and the oxidiser, which
supplies the oxygen needed for combustion. Liquid hydrogen, liquid paraffin etc.,
are used as rocket fuels and hydrogen peroxide, liquid oxygen etc., are used as
oxidisers. The fuel-oxidiser combination in a rocket is called the propellant.
The simplest form of a rocket consists of a combustion chamber in which a solid or
liquid propellant is burnt. There is a nozzle at its tail through which the gaseous
products of combustion can escape. The rocket forces a jet of hot gases
downwards through the nozzle. This is the action. The jet of gases exerts an equal
force on the rocket, pushing it forward. This is the reaction. This force gives the
rocket a forward acceleration.
With a single stage rocket it is not possible to attain very high speed and hence
multistage rockets are designed. In multistage rockets when the fuel of the first
stage gets exhausted, the rocket casing is detached and dropped off and the
second stage is ignited.

9. NUMERICALS
Q1.
A force of 980 N acts on a body for 0.1 seconds. Calculate the
change in momentum of the body.
Solution:
Force = 980 N
Time for which the force acts = 0.1 s
Change in momentum = impulse = Ft
Therefore, change in momentum = Ft
= 980 x 0.1
= 98 N S

10. Q2
A body of mass 10 kg moving with a velocity of 20 m/s along a straight line
collides with another body of mass 8 kg moving in the same direction with a
velocity of 5 m/s. After collision the velocity of the heavier body is 10 m/s.
Calculate the final velocity of the other.
Solution:
By law of conservation of momentum, momentum before collision is equal to
momentum after collision.
m1 u1 + m2 u2 = m1 v1 + m2 v2
10 x 20 + 8 x 5 = 10 x 10 + 8 x v2
200 + 40 = 100 + 8v2
240 = 100 + 8v2
8v2 = 240 - 100
8v2 = 140
i.e., velocity of the lighter body = 17.5 m/s