The Rotational Inertia of a Merry Go Round

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SUMMARY

The discussion centers on calculating the rotational inertia of a merry-go-round modeled as a disk with a mass (M) and radius (R=2.15m). The initial angular speed is 1.55 rad/s, which decreases to 1.45 rad/s as a boy (m1=58 kg) runs from the center to the edge while a girl (m2=45.2 kg) jumps off. The user initially attempted to apply the conservation of angular momentum using the equations IiWi=IfWf and If=1/2 Mr^2, but faced issues with mass cancellation. The correct approach requires careful setup of the equations to avoid errors in mass representation.

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Homework Statement


A merry go round modeled as a disk of mass M and radius R=2.15m is rotating in a horizontal plane about a frictionless vertical axle. Two youngsters are playing on the merry go round. The boy (m1=58 kg) is at the centre of the merry go round and the girl is at the edge - (m2=45.2 kg). The initial angular speed of the system is 1.55 rad/s. The girl sticks her tongue out at the boy and the boy chases her, running radially outward from the centre. By the time the boy gets to the edge the girl has jumped off. The angular speed reduces to 1.45 rad/s. Find the rotational inertia I and the mass M of the merry go round.


Homework Equations


I used IiWi=IfWf and set If=1/2 Mr^2 and Ii=1/2Mr^2 + m1r^2+m2r^2

However, I am not setting it up right because the masses cancel out, making it impossible for me to find the mass. I'm unsure of how to proceed.
 
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hi acg515! welcome to pf! :smile:

(have an omega: ω and try using the X2 and X2 buttons just above the Reply box :wink:)
acg515 said:
I used IiWi=IfWf and set If=1/2 Mr^2 and Ii=1/2Mr^2 + m1r^2+m2r^2

However, I am not setting it up right because the masses cancel out, making it impossible for me to find the mass. I'm unsure of how to proceed.

they shouldn't cancel :confused:

show us your full calculations, and then we'll see what went wrong, and we'll know how to help :smile:

(oh, and your m1r2 is in the wrong equation)
 

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