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

[quickclick330]

[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?

 

[Shooting Star]

Can you think of any quantity which will remain conserved?

 

[quickclick330]

The moment of inertia?

 

[Shooting Star]

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.

 

[quickclick330]

so initial and final angular momentum should equal since there is no external torque on the system right?

 

[Shooting Star]

You said it.

 

[quickclick330]

Thanks!

 

[quickclick330]

I do have one more question...how do u recalculate the new moment of inertia?

 

[Shooting Star]

MI of the mass = mass*(dist from axis)^2
Final MI = MI of disk + MI of the mass

 

[quickclick330]

okay, thanks