A student sits on a rotating stool holding two 4.0 kg objects. When his arms are
ID: 1744830 • Letter: A
Question
A student sits on a rotating stool holding two 4.0 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 3.0kg·m2 and is assumed to beconstant. The student then pulls the objects horizontally to0.40 m from the rotation axis. (a) Find the new angular speed of thestudent.1 rad/s
(b) Find the kinetic energy of the student system before and afterthe objects are pulled in. before 2 J after 3 J (a) Find the new angular speed of thestudent.
1 rad/s
(b) Find the kinetic energy of the student system before and afterthe objects are pulled in. before 2 J after 3 J before 2 J after 3 J
Explanation / Answer
Given that the mass of two objects is m = 4.0 kg Initial distance between the mass and axis of rotation is d1 = 1.0m Initialangular velocity is 1 = 0.75 rad/s momentof inertia of stool + student is I = 3.0 kg.m2 Initialdistance between the mass and axis of rotation is d2 = 1.0m -------------------------------------------------------------------------- Since there is no external force on the system then the angularmomentum is conserved initial angular momentum = final angular momentum (I + 2md12 )1 = (I + 2md22 )2 Then 2 = ( I + 2md12 )1/ ( I +2md22 ) = ---------- rad/s The kinetic energy before collsion isK1 = (1/2)( I + 2md12)12 =------------ J The kinetic energy beforecollsion is K2 = (1/2)( I + 2md22)22 =------------ J =------------ J The kinetic energy beforecollsion is K2 = (1/2)( I + 2md22)22 =------------ J =------------ JRelated Questions
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