In a playground there is a small merry-go-round of radius 1.48 m and mass 175 kg. The radius of gyration is 0.944 m. A child of mass 41.8 kg runs at a speed of 3.64 m/s tangent to the rim of the merry-go-round while it is at rest, and then jumps on. Find the angular velocity (in radians/second) of the merry-go-round and child together. Neglect friction.

Find the steady-state temperature at the center of the plate = /2, = /2) for sums of w from n=1 to n=19 (only odd values). find the value of n for which the change in /2, /2) is less than 1% from the value at the previous n. at this point, we consider the solution converged. does the value of the temperature at the center seem reasonable? in this part, the values of x and y are constant scalar values. you should produce a plot of the value of n on the horizontal and the estimate of the temperature at the center of the plate on the vertical. b. using the value of n (or larger) that resulted in convergence in part (a), create a contourf plot of the temperature distribution across the entire plate. use enough spatial subdivisions to create a useful plot. comment on the results. hint: you need to determine what “x” and “y” values to use to make your t matrix. i recommend using a different number of x and y values. use enough x and y values so that the plot is “smooth”.