A student on a piano stool rotates freely with an angular speed of2.98 rev/s. Th
ID: 1743137 • Letter: A
Question
A student on a piano stool rotates freely with an angular speed of2.98 rev/s. The student holds a1.41 kg mass in each outstretched arm,0.759 m from the axis of rotation. The combined moment of inertiaof the student and the stool, ignoring the two masses, is4.34kg·m2, a value that remainsconstant. (a) As the student pulls his arms inward, hisangular speed increases to 3.54 rev/s. How far are the masses fromthe axis of rotation at this time, considering the masses to bepoints?1 m
(b) Calculate the initial and final kinetic energy of thesystem.
2 J (initial)
3 J (final) (a) As the student pulls his arms inward, hisangular speed increases to 3.54 rev/s. How far are the masses fromthe axis of rotation at this time, considering the masses to bepoints?
1 m
(b) Calculate the initial and final kinetic energy of thesystem.
2 J (initial)
3 J (final)
Explanation / Answer
= 2.98 rev/s = 2.98*2 rad/s.m = 1.41 kg, a = 0.759 m, I = 4.34 kg·m2, (a) ' = 3.54 rev/s = 3.54*2 rad/s. find x (I + 2ma2) = (I + 2mx2)' x = 0.491 m (b) the initial kinetic energy of the system = (I +2ma2)2/2 = 1.03*103 J final kineic energy of the system = (I +2mx2)'2/2 = 1.24*103 J
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