Does angular momentum change with radius?

1 Answer

Answer:

Yes, angular momentum of a rotating body changes with radius.

Explanation:

The angular momentum # \vec J# of a point mass #m# rotating with a linear velocity #\vec v# at a radius #\vec r# about an axis is given as

#\vec J=m(\vec r\times \vec v)#

In scalar form, the angular momentum #J# of a point mass #m# rotating with an angular velocity # omega# at a radius #r# about an axis is given as

#J=mvr#

#J=m(r\omega)r#

#J=mr^2\omega#

#J\prop r^2#

The above equation shows that the angular momentum of a rotating body varies with the square of radius #r#.

In case of an extended body #r# is the distance of center of mass from the axis of rotation.