Question
Show that angular momentum of a rotating body is equal to product of radial distance of point of particle from the axis of rotation and transverse component of linear momentum or it is equal to the product of the linear momentum and perpendicular distance of direction of motion from the axis of rotation.
Solution
Consider a particle moving in the space.
Let at any instant t, the particle be at A.
Let 
be the velocity of particle at A and 
be the position vector.
The angular momentum of particle is, 
Magnitude of angular momentum, 
where,
be the angle which 
makes with 
.
Now,
where,
pϕ is transverse component of angular momentum.
Therefore, angular momentum is equal to product of radial distance and transverse component of linear momentum.
Also L = r p sin ϕ
= sin ϕ)
= pd
Therefore, angular momentum is equal to product of the magnitude of angular momentum and perpendicular distance of direction of motion from the axis of rotation.
