small distance above it and immediately sticks to the turn- table at a point 1.8
ID: 1782309 • Letter: S
Question
small distance above it and immediately sticks to the turn- table at a point 1.80 m to the east of the axis. (a) Find the final angular speed of the clay and turntable. (b) Is the mechanical energy of the turntable-clay system constant in this process? Explain and use numerical results to verify your answer. (c) Is the momentum of the system constant in this process? Explain your answer. 34. A student sits on a freely rotating stool holding two dumb- bells, each of mass 3.00 kg (Fig. P11.34). When his arms are extended horizontally (Fig. P11.34a), the dumbbells are 1.00 m from the axis of rotation and the student rotates B with an angular speed of 0.750 rad/s. The moment of iner- tia of the student plus stool is 3.00 kg m2 and is assumed to be constant. The student pulls the dumbbells inward horizontally to a position 0.300 m from the rotation axis (Fig. P11.34b). (a) Find the new angular speed of the stu- dent. (b) Find the kinetic energy of the rotating system before and after he pulls the dumbbells inward. Figure P11.34Explanation / Answer
a)initial mass moment of inertia of system about axis of rotation = 3+2*(3*12)=9 kg-m2
initial angular velocity = 0.75 rad/s
Final mass moment of inertia of system = 3+2*(3*0.32)=3.54 kg-m2
Let final angular velocity be w
From conservation of angular momentum,
9*0.75=3.54*w
w= 9*0.75/3.54=1.91 rad/s
b)Initial rotational kinetic energy = 0.5*9*0.752=2.53 Joules
Final rotational kinetic energy = 0.5*3.54*1.912=6.46 Joules
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