A student sits on a rotating stool holding two 2.3-kg objects. When his arms are

Question

A student sits on a rotating stool holding two 2.3-kg objects. When his arms are extended horizontally, the objects are 1.0 m from the axis of rotation and he rotates with an angular speed of 0.75 rad/s. The moment of inertia of the student plus stool is

3.0 kg · m2

and is assumed to be constant. The student then pulls in the objects horizontally to 0.46 m from the rotation axis.

(a) Find the new angular speed of the student.
rad/s

(b) Find the kinetic energy of the student before and after the objects are pulled in.

Explanation / Answer

the inital momnet of inertia of object is 2*2.3*1*1 = 4.6kgm^2

hence angular momentum = (4.6+ 3)*0.75 = 5.7

new momne tof inertia of objects is 2*2.3*0.46*0.46 = 0.97336

by cinservation of angular momentum new angular velocity = 5.7/(3+0.97336) = 1.4344

kinetic energy before = 1/2*7.6*0.75*0.75 = 2.1375

kinetic energy after = 1/2*3.97366*1.4344*1.4344 = 4.087

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