Thursday, November 19, 2009

Student's mass?

A physics student is standing on an initially motionless, frictionless turntable with rotational inertia 0.31 kg·m2. He's holding a wheel of rotational inertia 0.22 kg·m2 spining at 133 rpm about a vertical axis, as we showed in Fig. 11.8. When he turns the wheel upside down, student and turntable begin rotating at 63 rpm.





(a) What is the student's mass, considering him to be a cylinder 30 cm in diameter?


(b) How much work did he do in turning the wheel upside down? Neglect the distance between the axes of the turntable and wheel.

Student's mass?
You cannot do this problem unless you assume the wheel does not change its speed as the student flips it over.





IF you assume that, then this is what you do:





Let L_wheel = angular momentum of wheel = Iw [I= moment of inertia = .22 kgm^2, w = angular momentum = 133*2PI/60].





The change in angular momentum is 2L [because the wheel is going from spinning clockwise to spinning counter-clockwise].





This change in angular momentum must be matched by the angular momentum gained by the turntable and the student.





L_table = Iw , I= .31kgm^2, w =63*2PI/60





L_student = Iw, I=1/2mr^2, w = 63*2PI/60, r = .15 m





Set L_table + L_student = 2L_wheel and solve for mass.





To find work, just calculate the kinetic energy gained by the student and table:


KE_student = 1/2 Iw^2, KE_table = 1/2Iw^2





The work is equal to the gain in kinetic energy.

tooth fairy

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