**Angular momentum**

Angular momentum is defined as the moment of linear momentum of an object. It is denoted by L.

According to definition,

L = p. r

L = m. v. r

L = m. r. ω. r

L = m. r

^{2}. ω is the expression for angular momentum of the body**Relationship between Angular momentum and moment of inertia**

Let a body is mass ‘M’ made up of n-particles rotate about the axis YY'. Let us suppose small particles m

_{1}, m_{2}, m_{3}, ……, m_{n}and the distance between YY' and distance between YY' and it be r_{1}, r_{2}, r_{3}, …... respectively.We know angular velocity of all the particles are same but linear velocity is different due to the different position of particles. Then, Linear velocity of m

_{1}is given by v

_{1}= r_{1}ωSimilarly,

v

_{2}= r_{2}ω v

_{3}= r_{3}ωThe angular momentum of mass m

_{1}is, L = Linear momentum * r_{1}L = m

_{1}*v_{1}*r_{1}L = m

_{1}*r_{1}^{2}*ωSimilarly, the angular momentum of masses m

_{2}, m_{3}, …..,m_{n}are m_{2}*r_{2}^{2}*ω, m_{3}*r_{3}^{2}*ω, m_{n}*r_{n}^{2}*ω,The total angular momentum of the body is L = m

_{1}r_{1}^{2}ω + m_{2}r_{2}^{2}ω + m_{3}r_{3}^{2}ω + …………... + m_{n}r_{n}^{2}ω L = ω (m

_{1}r_{1}^{2}+ m_{2}r_{2}^{2}+ m_{3}r_{3}^{2}+ …………... + m_{n}r_{n}^{2}) L = I. ω

## Share on Social Media