What is the new rotation time of the merry-go-round?

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The discussion focuses on calculating the new rotation time of a playground merry-go-round after adding a mass. Initially, the merry-go-round completes a revolution in 0.5 seconds with a moment of inertia of 50 kg m². When a 5 kg block is added at a distance of 1.0 m from the center, the angular momentum is conserved since no external torque acts on the system. Participants discuss how to recalculate the new moment of inertia by adding the moment of inertia of the block to that of the merry-go-round. The final rotation time is determined based on the new moment of inertia and the conservation of angular momentum.
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[SOLVED] Not sure where to start...

10. A playground merry-go-round is mounted on a frictionless axle, so it can only rotate
in the horizontal plane. This object has a moment of inertia about the axle of I=50 kg m2,
and it has a diameter of 2.2 meters. Initially it is turning at a constant rate so that it
completes one revolution in 0.5 seconds. Standing next to it, you carefully place a block
of mass m= 5.0 kg on the rotating table, so that it sits a distance r=1.0 m from the center.
How long does it take to complete one rotation now?
1. 0.5 s
2. 0.55 s
3. 0.59 s
4. 0.63 s
5. 0.67 s
6. 0.71 s

all i have is that i found wi = 12.57 rad/s...but i don't know what to do after that?
 
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Can you think of any quantity which will remain conserved?
 
The moment of inertia?
 
No, because the mass distribution has changed after you put the mass on it.

If there's no external torque on a body, then the angular momentum remains the same. So, you should find the initial and final angular momenta.
 
so initial and final angular momentum should equal since there is no external torque on the system right?
 
You said it.
 
Thanks!
 
I do have one more question...how do u recalculate the new moment of inertia?
 
MI of the mass = mass*(dist from axis)^2
Final MI = MI of disk + MI of the mass
 
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okay, thanks
 
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