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The motor and breaks en a Merry-Go-Round (carousel) have faded, leaving the 1000kg approximately-uniform disk to rotate at a constant speed of 10 RPM
The motor and breaks en a Merry-Go-Round (carousel) have faded, leaving the 1000kg approximately-uniform disk to rotate at a constant speed of 10 RPM. In order to safely rescue the nearly massless children, the carnie informs the groups of concerned parents that the translational speed at the edge of the carousel must be no more than 2m/s. The carnie then gives an important lesson on angular momentum, instructing them to jump onto the outside edge of the 10-meter diameter carousel to reduce its speed. Using his supernatural carnie weigh, estimation skills, he determines the average mass of the parents to be 80kg. How many parents must he convince to jump onto the carousel such that the children can be safely rescued?
Expert Solution
We have given that,
Mass of carousel (m)=1000kg(m)=1000kg
Radius of carousel (r)=5m(r)=5m
Initial angular speed ωi=10rpm=2π×1060=1.047rad/secωi=10rpm=2π×1060=1.047rad/sec
Final angular speed ωf=Vr=25=0.4rad/secωf=Vr=25=0.4rad/sec
Let us assume that,
nn Parent jump to get the speed to 2m/sec2m/sec
According to question,
The conservation of angular momentum is given by
Iωi=Iωf+n(mpvr)12mr2ωi=12mr2ωf+n(mpvr)12×1000×52×1.047=12×1000×52×0.4+n(80×2×5)n=10.109n≈11Iωi=Iωf+n(mpvr)12mr2ωi=12mr2ωf+n(mpvr)12×1000×52×1.047=12×1000×52×0.4+n(80×2×5)n=10.109n≈11
Hence, 1111 parents must be convinced to jump.
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