A student sits on a rotating stool holding two 3.0 kg objects. When his arms are
ID: 1723741 • Letter: A
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.
Explanation / Answer
(a) from the given problem the total anguar momentumof the system of the student the stool and the weights about the axis of rotation is givenby Itotal = Iweights +Istudent = 2 (m r2) + 3.00 kg . m2 intially we get r = 1.00 m Ii = 2 (3.00 kg) (1.00 m)2+ 3.00 kg . m2 = ........ kg .m2 finally r = 0.200 m If = 2 (3.00 kg) (0.200 m)2+ 3.00 kg . m2 = ........ kg .m2 according to the law of conservation of momentumwe get If f =Ii i solve for f f = ........ rad / s (b) KEi = (1 / 2) Iii2 =........ J KEf = (1 / 2) Iff2 =........ J =........ J
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