A horizontal 810-N merry-go-round of radius 1.30 m is started from rest by a con

Question

A horizontal 810-N merry-go-round of radius 1.30 m is started from rest by a constant horizontal force of 45 N applied tangentially to the merry-go-round. Find the kinetic energy of the merry-go-round after 3.0 s. (Assume it is a solid cylinder.)

Explanation / Answer

I alpha = F R ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ ==> alpha = FR/I = FR/(0.5 M R^2) = 45*1.3/(0.5*(810/9.81)*1.3*1.3) = 0.83846 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ ==> w = alpha t = 0.83846 * 3 = 2.51538 rad/s ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ ==> K = 0.5 I w^2 = 0.5 * (0.5*(810/9.81)*1.3*1.3) * 2.51538 * 2.51538 = 221 J

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