Question 8.18: THE MERRY-GO-ROUND GOAL Apply conservation of angular moment...
THE MERRY-GO-ROUND
GOAL Apply conservation of angular momentum while combining two moments of inertia.
PROBLEM A merry-go-round modeled as a disk of mass M=1.00 \times 10^{2} \mathrm{~kg} and radius R=2.00 \mathrm{~m} is rotating in a horizontal plane about a frictionless vertical axle (Fig. 8.37 is an overhead view of the system). (a) After a student with mass m=60.0 \mathrm{~kg} jumps on the rim of the merry-go-round, the system’s angular speed decreases to 2.00 \mathrm{rad} / \mathrm{s}. If the student walks slowly from the edge toward the center, find the angular speed of the system when she reaches a point 0.500 \mathrm{~m} from the center. (b) Find the change in the system’s rotational kinetic energy caused by her movement to r=0.500 \mathrm{~m}. (c) Find the work done on the student as she walks to r=0.500 \mathrm{~m}.
STRATEGY This problem can be solved with conservation of angular momentum by equating the system’s initial angular momentum when the student stands at the rim to the angular momentum when the student has reached r=0.500 \mathrm{~m}. The key is to find the different moments of inertia.
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