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**Problem:**

In a plyground there is a small merry-go-round of radius 3.91 m and rotational inertia 5.68e+03 kg m^2. A child of mass 199 kg runs at a speed of 3.09 m/sec tangent to the rim of the merry-go-round when it is at rest and then jumps on. Assume no friction in the bearing of the merry-go-round. What is the angular velocity of the merry-go-round and child?

Besides the child be a heavy example, I wasn't able to come up with the right answer of 0.276 rad/sec. What might I be doing wrong?

**My Work:**

I searched the archives and found two ways of solving the problem.

[tex]method \ 1 \ \Rightarrow m*v*r = (I_{merry-go-round} + I_{child}) \omega \ ; solving \ for \ \omega[/tex]

[tex]method \ 2 \ \Rightarrow I_{merry-go-round} * \omega \ + \ m*v*r = (I_{merry-go-round} + I_{child}) \omega^{prime} \ ; \ solving \ for \ \omega^{prime}[/tex]

What I came up with:

[tex]method \ 1 \ \Rightarrow (199 kg \ + (\frac{5680 kg*m^{2}}{3.91m^{2}}))*(3.09 \frac{m}{sec})*(3.91m) = ((5680 kg*m^{2}) + (199 kg * ((3.91m)^{2}))) \omega \ ; solving \ for \ \omega[/tex]

[tex]\omega \ = \ 2.87[/tex]

[tex]method \ 2 \ \Rightarrow ((5680 kg*m^{2}) * (\frac{3.09 \frac{m}{sec}}{3.91 m} * 2 \pi)) + (199 kg \ + (\frac{5680 kg*m^{2}}{(3.91m)^{2}})*(3.09 \frac{m}{sec})*(3.91m) = (5680 kg*m^{2} + (199 kg * (3.91m^{2})) \omega^{prime} \ ;[/tex]

[tex]solving \ for \ \omega^{prime}[/tex]

[tex]\omega^{prime} \ = \ 5.52[/tex]