A student sits on a rotating stool holding two 3.6-kg objects. When his arms are

Question

A student sits on a rotating stool holding two 3.6-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 0.47 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:

after:

Explanation / Answer

conservation of angular momentum
3*.75 + 2*3.6*1^2*.75 =( 3 +2*3.6*.47^2)

a)

new angular speed of the student = 1.67 rad/s

b)

To be precise we can calculate teh kinetic energy of the student ,because moment of inertia of the student is not given. We can calculate the kinetic energy of student+stool

Kinetic energy of the student+stool before .5I^2=.5*3*.75^2 = .84375

after = .5*3*1.67^2 = 4.18335

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