Question

A student on a piano stool rotates freely with an angular speed of 3.07 rev/s. The student holds a 1.38 kg mass in each outstretched arm, 0.759 m from the axis of rotation. The combined moment of inertia of the student and the stool, ignoring the two masses, is 4.72 kg·m2, a value that remains constant.

a. As the student pulls his arms inward, his angular speed increases to 3.54 rev/s. How far are the masses from the axis of rotation at this time, considering the masses to be points?

b. Calculate the initial and final kinetic energy of the system.

Answer 1

This is a conservation of angular momentum question.
Li = I1 omegai + I2 omegai
I1 given
I2 = mr^2 times 2 (since 2 books)
omegai is the same for both (convert to rad/sec)
Lf = I1 omegaf + I2 omegaf
compute new I2
Li=Lf and solve for omegaf
b) KEi = 1/2I1 omegai^2 + 1/2I2 omegai^2

do same for KEf