# Is angular momentum conserved radially in a rotating body?

How does the conservation of angular momentum work radially with respect to a rotating body?

For example, if a rotating body, such as a spinning top, were to lose an outer layer or shell, would it continue rotating at the same rate, or would it speed up or slow down?

• Does the outer layer itself keep spinning or is it brought to rest somehow? This seems reminiscent of spinning stars losing outer layers. – jacob1729 Mar 4 '19 at 12:18
• Calculate the total angular momentum of the system before the outer layer is lost. Then assert that the total angular momentum of the system (spinning top plus outer layer) is the same immediately after they lose contact with each other. What happens to the top is whatever is necessary to hold that assertion and, therefore, depends on exactly how the outer layer is lost – Jim Mar 4 '19 at 14:08

Angular momentum is the rotational analogue of linear momentum with the formula: $$L=I\omega$$ It can also be further derived as: $$L=(mr^2)\left(\frac vr \right)=mvr$$
$$r$$ being the radius from the center of the mass to the rim, then we can logically deduce that angular momentum is directly proportional to angular velocity and angular velocity is inversely proportional to the radius. So if the angular momentum is conserved, an increase or decrease in radius translates to a decrease or increase in angular velocity respectively.