A student sits on a rotating stool holding two 3.0 kg objects. When his arms are

Question

A student sits on a rotating stool holding two 3.0 kg objects. When his arms are extendedhorizontally, the objects are 1.0 m from the axis of rotation, andhe rotates with an angular speed of 0.75 rad/s. The moment ofinertia of the student plus stool is 3.0 kg·m2and is assumed to be constant. The student then pulls the objectshorizontally to 0.20 m from the rotationaxis.

(a) Find the new angular speed of the student

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

after

Explanation / Answer

moment of inertia of the systembefore is I1=3+2*3*1=9kgm2. moment of inertia of the system after isI2=3+2*3*.2*.2=3.24kgm2. a) applying conservation of angular momentum: I11=I22; 2=9*0.75/3.24=2.083 rad/s. b) the kinetic energy of the student before is1/2*9*.752=2.5312J; the kinetic energy of the student after is1/2*3.25*2.083*2.083=7.052J;

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