Part one

a student sits on a rotating stool holding two
2 kg objects. when his arms are extended
horizontally, the objects are 1 m from the axis
of rotation, and he rotates with angular speed
of 0.73 rad/sec. the moment of inertia of the
student plus the stool is 8 kg m2
and is assumed to be constant. the student then pulls
the objects horizontally to a radius 0.28 m
from the rotation axis.
calculate the final angular speed of the
student.
answer in units of rad/s.
(use pictures)

part two
calculate the change in kinetic energy of the
system.
answer in units of j.

Answers:

a)

b)

Explanation:

a) Final angular velocity :

Before solving this part, we have to stay clear that the angular momentum is conserved, since we are dealing with circular motion, then:

Hence:

(1)

Where:

is the initial moment of inertia of the system

is the initial angular velocity

is the final moment of inertia of the system

is the final angular velocity

But first, we have to find and :

(2)

(3)

Where:

is the student's moment of inertia

is the mass of each object

is the initial radius

is the final radius

Then:

(4)

(5)

Substituting the results of (4) and (5) in (1):

(6)

Finding :

 (7) This is the final angular speed

b) Change in kinetic energy:

The rotational kinetic energy is defined as:

(8)

And the change in kinetic energy is:

(9)

Since we already calculated these values, we can solve (9):

(10)

Finally:

This is the change in kinetic energy

the displacement produced by the body.  

the amount of force subjected to the body.  

the angle between the direction of force and displacement