# Separation of Mot

A. Take a system of I moving particles:

Mass of the ith particle = mi

Velocity of the ith particle = vi

momentum of the ith particle, pi = mivi

Velocity of the canter of the mass = V

Thus, velocity of the ith particle with respect to canter of the mass, vi’ = vi – V …..(1)

Multiplying mi throughout the equation (1) we get,

mivi’ = mivi – miV

pi’ = pi - miV

Where,

pi’ = momentum of the ith particle with respect to the canter of the mass.

Taking the summation of the momentums of the all the particle with respect to the canter the mass of the body,

…..(2)

Where,

ri’ = position of the ith particle with respect to the canter of mass and,

As per the definition of the canter of the mass, we have,

from equation 2,

B. We have the relation for velocity of the particle as,

…..(3)

Taking the dot product with itself will give,

Here, For the canter of mass of the system of the particle,

Therefore,

C. Total angular momentum of the system of the particles,

The las two terms vanish for both contain the factor which is equal to zero from the definition of the center of the mass. Also,

So that,

D. From the previous solution,

( ) Total toque,

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation view all courses RELATED QUESTIONS :

Separation of MotNCERT - Physics Part-I

A hoop of radius NCERT - Physics Part-I

A 60 kg man skatiHC Verma - Concepts of Physics Part 1

A ball of mass 0.HC Verma - Concepts of Physics Part 1

A man of mass M hHC Verma - Concepts of Physics Part 1

A neutron initialHC Verma - Concepts of Physics Part 1

A ball of mass 50HC Verma - Concepts of Physics Part 1

Light in certain HC Verma - Concepts of Physics Part 1

A uranium-238 nucHC Verma - Concepts of Physics Part 1

Find the ratio ofHC Verma - Concepts of Physics Part 1