# Conservation of angular momentum and consequential changes in rotational kinetic energy Suppose for example consider the following abstract example, a circular disk that has several objects joined to it via short weak thin strings is made to rotate about an axis with an initial angular velocity = w0

A pole attached to the axis and extended further has a very sharp knife oriented in the plane of rotation that starts sliding down simultaneously with the beginning of rotation

When it reaches the required height, the strings begin to get cut and the particles fly off with respective linear momentum and kinetic energies corresponding to the linear velocities they had at the time of detachment (v= w0r) Thus the magnitude of kinetic energy for each individual particle remains the same (considering their initial moi = mr^2)

However at the instant that all the n objects have left the system the rotational kinetic energy of the disk that remains is more than the combined total kinetic energy earlier

Ei= (1/2)(I+ni)(w0)^2

wf= (I+ni)(w0)/I ... (conserv. ang. momen.)

Ef= [((I+ni)(w0))^2]/2I > Ei

How does this come about as there is no external force present to produce the necessary torque? Does the impact with the blade produce the required torque? Or have i misunderstood some concept?