A student sits on a rotating stool holding two 3.0-kg objects. when his arms are
ID: 1751420 • Letter: A
Question
A student sits on a rotating stool holding two 3.0-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 x m^2 and is assumed to be constant. the student then pulls in the objects horizontally to 0.30 m from the rotation axis. (a) find the new angular speed of the student. (b) Find the kinetic energy of the student before and after the objects are pulled in.Explanation / Answer
Given Mass of object m = 3.0 kg moment of inertia I1 of the system I1 =3.0kgm2 angular speed 1 = 0.75 rad/s distance of object from axis of rotation = 1.0m - 0.30m = 0.70m a) moment of inertia of system I2 =I1+[2{mr2}] here r = 1.0m thus I2 ' =I1+[2{mr2}] calculate for I2' here r = 0.30m thus I2 " =I1+[2{mr2}] calculate for I2" According to the law of conservation of angular momentum I2'1 =I2"2 the new angular speed of the student is 2 =I2'1/I2" =------------- b) the kinetic energy of the student before the the objects arepulled in [KEstud]before =1/2*I2'12 = ----------- the kinetic energy of the student after the the objectsare pulled in [KEstud]after = 1/2*I2"22 = ----------- calculate for I2" According to the law of conservation of angular momentum I2'1 =I2"2 the new angular speed of the student is 2 =I2'1/I2" =------------- b) the kinetic energy of the student before the the objects arepulled in [KEstud]before =1/2*I2'12 = ----------- the kinetic energy of the student after the the objectsare pulled in [KEstud]after = 1/2*I2"22 = ----------- the kinetic energy of the student after the the objectsare pulled in [KEstud]after = 1/2*I2"22 = -----------Related Questions
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