A student sits on a rotating stool holding two 3.0 kg objects. When his arms are
ID: 1723564 • 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.1 rad/s
(b) Find the kinetic energy of the student before and after theobjects are pulled in. before 2 J after 3 J before 2 J after 3 J
Explanation / Answer
Given that the mass of each object is m = 3.0 kg initial distance between each object and axis of rotation isd = 1.0 m final distance between each object and axis ofrotation is x = 0.20 m initial angular velocity is = 0.75 rad/s The moment of inertia of the student plus stool is I = 3.0kg·m2 ------------------------------------------------------------------------------------ Since there is no external torque on thesystem so the angular momentum is conserved initial angular momentum = total final angularmomentum ( I +md2) = ( I +mx2)f f = ( I + md2) / ( I +mx2) = ----------- rad/s Kinetic energy of the student before is K1 = (1/2)( I +md2)2 = ------------ J Kinetic energy of the student after is K2 = (1/2)( I +mx2) f2 = ------------ J
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