Question

A merry-go-round with a moment of inertia of 750 kgm^2 and a radius of 2.55 m is rotating with an angular velocity of 9.42 rad/s clockwise (as viewed from above.) A child, whose weight is 334 N, runs at 2.76 m/s tangent to the rim of the merry-go-round and jumps onto it in the direction opposite of its sense of rotation. With what angular speed does the merry-go-round rotate after the child jumps onto its edge?

I'm pretty sure the answer is going to be negative.

Answer 1

I'm pretty sure the answer is going to be negative. Let's see  

apply angular momentum conservation

mg = 334 N

m = 334/9.8 = 34.0816327 kg  

Li = Lf  

rX P + I*ωi = ( I_total ) *ωf

-2.55*(34.0816327*2.76) + 750*2.55^2/2 *9.42 = ( 34.0816327 *2.55^2 + 750*2.55^2/2)*ωf

ω≈8.54502 rad/s answer  

you were saying the answer will be negative   Well it will depend on which direction you are taking positive and which is as negative there is no hard rule about it  

generally we take clockwise as negative  

by that sense you are the correct answer will be negative  

ω≈ -8.54502 rad/s answer  

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