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 0.26 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

Explanation / Answer

Conservation of angular momentum

(3+4.6)*0.75 =(3+1.196)*

= 1.36 rad/s

b) before, K.E. = 0.5 *3*0.752 + 0.5*2.3*2*0.752 

                    = 2.14 J

after K.E.  = 0.5*3*1.362 + 0.5*2.3*2*1.362*0.262

               = 3.06 J

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