A merry-go-round has a moment of inertia of 400 kg m² and turns freely at 1.0 rad/s…

Step 1. (a) $400\ \text{kg\,m}^2 \times 1.0\ \text{rad/s} = 497.2\ \text{kg\,m}^2\,\omega'$, so $\omega' = 0.805\ \text{rad/s}$.

Step 2. (b) Before: $\tfrac12 \times 400\ \text{kg m}^2 \times (1.0\ \text{rad/s})^2 = 200\ \text{J}$. After: $\tfrac12 \times 497.2\ \text{kg\,m}^2 \times (0.805\ \text{rad/s})^2 = 160.9\ \text{J}$. Lost: $39.1\ \text{J}$.