A student on a piano stool rotates freely with an angular speed of 2.85rev/s . The student holds a 1.10kg mass in each outstretched arm, 0.789m from the axis of rotation. The combined moment of inertia of the student and the stool, ignoring the two masses, is 5.23kg⋅m2 , a value that remains constant.

Question

--> As the student pulls his arms inward, his angular speed increases to 3.45rev/s . How far are the masses from the axis of rotation at this time, considering the masses to be points?

-->Calculate the initial kinetic energy of the system.

-->Calculate the final kinetic energy of the system.

bobpursley · Answer

Calculate the moment of inertia for the masses (2*mr^2)

now the student I and the mass I add to give Itotal, both in the initial Itotali, and the final Itotalf where one of them has a different radius0

conservation of momentum applies
Intial momentum=final momentum
(Itotali*2PI*2.85)=Itotalf*2PI*(3.45)
notice the 2PI divide out, so now solve for rfinal in the Itotalf.
iniial KE=1/2 Itotali*(2PI*2.85)^2 and similar for final KE