The Rotational Inertia of a Merry Go Round

[acg515]

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.

 

[tiny-tim]

welcome to pf!

hi acg515! welcome to pf!

(have an omega: ω and try using the X² and X₂ buttons just above the Reply box )

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

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

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