A student sits on a rotating stool holding two 3.7-kg objects. When his arms are

Question

A student sits on a rotating stool holding two 3.7-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·m2 and is assumed to be constant. The student then pulls in the objects horizontally to 0.29 m from the rotation axis (a) Find the new angular speed of the student. 2.15330428rad/s (b) Find the kinetic energy of the student before and after the objects are pulled in before 2.925 9.564484966 X Your response differs from the correct answer by more than 10%. Double check your calculations. J

Explanation / Answer

lnitial moment of inertia,

li = lo + 2mr^2

li = 3 + 2*3.7*1^2 = 10.4 kg.m^2

final moment of inertia,

lf = 3 + 2*3.7*(0.29)^2 = 3.62 kg.m^2

intial angular speed, wi = 0.75 rad/s

(a)

From conservation of angular moment,

li*wi = lf*wf

10.4*0.75 = 3.62*wf

wf = 2.153 rad/s

(b)

lnitial KE ,

KEi = (1/2)*li*wi^2

KEi = (1/2)*10.4*(0.75)^2

KEi = 2.925 J

(c)

Final KE after the objects are pulled,

KEf = (1/2)*lf*wf^2 = (1/2)*3.62*(2.153)^2

KEf = 8.397 J

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