Astudent sits on a rotating stool holding two 2.6-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 0.29 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.
before: j
after: j

(a)

(b)

before

after    

Explanation:

Given:

mass of each object,

initial stretch of arms from the center,

initial angular velocity,

moment of inertia of stool and the student together,

final stretch of arms from the center,

According to the law of conservation of angular momentum, initial angular momentum is equal to the final angular momentum in absence of any external  force.

(a)

(b)

We know,

Putting the initial values:

Kinetic energy before the objects are pulled in

Putting the final values:

Kinetic energy after the objects are pulled in

increases it