Question

A wheel is roatating freely at an angular speed of 800 rev/min on a Shaft of negligible moment of inertia. A second wheel initially at rest and with twice the moment of inertia of the first, is suddenly coupled to the same shaft. (a) what is the angular speed of the resultant combination of the shaft and two wheels? (b) What fraction of the original rotational kinetic energy is lost? Treat the wheels as hoops in your analysis

Answer 1

Angular momentum will conserved, and the total moment of inertia (I) is tripled. Since angular momentum is I*w, the angular spped w must be reduced to 1/3 of the original value.

With w reduced to 1/3 of the original and I tripled, the kinetic energy (1/2) I w^2 will be reduced to 1/3 the former value.