A wheel of moment of inertia I_(1)rotates about a vertical frictionless axle with an angular velocity omega_(1). A second wheel of moment of inertia I_2 and initially at rest drops onto the first wheel. The two wheels attain a common angular velocity of omega_(2) . (a) What is the value of omega_(2) ? (b) What is the ratio of the initial to the final rotational energy ?

A wheel of moment of inertia I_(1)rotates about a vertical frictionles

1.	A wheel of moment of inertia I_(1)rotates about a vertical frictionless axle with an angular velocity omega_(1). A second wheel of moment of inertia I_2 and initially at rest drops onto the first wheel. The two wheels attain a common angular velocity of omega_(2) . (a) What is the value of omega_(2) ? (b) What is the ratio of the initial to the final rotational energy ?
Answer» SOLUTION :`omega_(2)=I_(1)OMEGA(1)//I_(1) + I_(2), K.E_(i)//K.E_(F) =(1//2) I_(1)omega_(2)^(2) = I_(1) + I_(2)//I_(1)`