- Introduction
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- Center of Mass
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- Position of center of mass
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- Position vector of centre of mass in terms of co-ordinate components
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- Motion of centre of mass
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- Acceleration of centre of mass
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- Kinetic energy of the system of particles
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- Two particle system and reduced mass
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- Collisions
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- Head on elastic collision of two particles
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- Head on inelastic collision of two particles
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- Deflection of an moving particle in two dimension
- Solved examples

- Included with Linear momentum
- Assignment 1
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- Assignment 2
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- Assignment 3
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- Assignment 4

- Included with Linear momentum
- How to solve center of mass problems

- Until now we have focused on describing motion of a single particle in one, two or three dimensions. By particle we mean to say that it has a size negligible in comparison to the path raveled by it.

- When we studied Law's of motion we have applied them even to the bodies having finite size imagining that motion of such bodies can be described in terms of motion of particles.

- While doing so we have ignored the the internal structure of such bodies. Any real body we encounter in our daily life has a finite size and idealized model of particle is inadequate when we deal with motion of real bodies of finite size .

- Real bodies of finite size can also be regarded as the system of particles. While studying system of particles we will not concentrate on each and every particle of the system instead we will consider the motion of system as a whole.

- Large number of problems involving extended bodies or real bodies of finite size can be solved by considering them as
**Rigid Bodies**. We define rigid body as a body having definite and unchanging shape.

- A rigid body is a rigid assembly of particles with fixed inter-particle distances. In actual bodies deformations do occur but we neglect them for the sake of simplicity.

- In this chapter we will study about centre of mass of system of particles, motion of centre of mass and about collisions.

- Consider a body consisting of large number of particles whose mass is equal to the total mass of all the particles. When such a body undergoes a translational motion the displacement is produced in each and every particle of the body with respect to their original position.

- If this body is executing motion under the effect of some external forces acting on it then it has been found that there is a point in the system , where if whole mass of the system is supposed to be concentrated and the nature the motion executed by the system remains unaltered when force acting on the system is directly applied to this point. Such a point of the system is called centre of mass of the system.

- Hence for any system
**Centre of mass is the point where whole mass of the system can be supposed to be concentrated and motion of the system can be defined in terms of the centre of mass.**

- Consider a stationary frame of refrance where a body of mass M is situated. This body is made up of n number of particles. Let m
_{i}be the mass and**r**_{i}be the pisition vector of i'th particle of the body.

- Let C be any point in the body whose position vector with respect to origin O of the frame of refrance is
**R**_{c}and position vector of point C w.r.t. i'th particle is**r**_{ci}as shown below in the figure.

- From triangle OCP

**r**_{i}=**R**_{c}+**r**_{ci}(1)

multiplying both sides of equation 1 bt m_{i}we get

m_{i}**r**_{i}=m_{i}**R**_{c}+m_{i}**r**_{ci}

taking summation of above equation for n particles we get

If for a body

then point C is known as the centre of mass of the body.

- Hence a point in a body w.r.t. which the sum of the product of mass of the particle and their position vector is equal to zero is equal to zero is known as centre of mass of the body.

- Consider a system made up of two particles whose mass are m
_{1}and m_{2}and their respective position vectors w.r.t. origin O be**r**_{1}and**r**_{2}and**R**_{cm}be the position vector of centre of mass of the system as shown below in the figure. So from equation 2

- If M=m
_{1}+m_{2}=total mass of the system , then

- Consider a many particle system made up of number of particles as shown below in the figure. Let m
_{1}, m_{2}, m_{3}, . . . . . . . . . . . . . , m_{n}be the masses of the particles of system and their respective position vectors w.r.t. origin are**r**_{1},**r**_{2},**r**_{3}, . . . . . . . . . . . . . . . . . ,**r**_{n}.

Also position vector of centre of mass of the system w.r.t. origin of the reference frame be**R**_{cm}then from equation 2

- Because of the definition of centre of mass

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