Calculate the rotational kinetic energy of the system of platform plus person be

Question

Calculate the rotational kinetic energy of the system of platform plus person before and after the person's walk Constants A person of mass 79 kg stands at the center of a rotating merry-go-round platform of radius 2.7 m and moment of inertia 810 kg m2. The platform rotates without friction with angular velocity 0.95 rad/s. The person walks radially to the edge of the platform. Express your answers using two significant figures. Enter your answers numerically separated by a comma. KE, KEf SubmitPrev X Incorrect, One attempt remaining; Try Again; no points deducted Previous Answers RequestAnswer Your answer does not have the correct number of comma-separated terms.

Explanation / Answer

m = mass of person = 79 kg

ri = initial distance of person from center = 0 m

Ipi = initial moment of person when at the center = m ri2 = (79) (0)2 = 0

rf = fina; distance of person from center = 2.7 m

Ipf = final moment of person when at the edge = m rf2 = (79) (2.7)2 = 575.91 kgm2

I = moment of inertia of merry-go-round = 810

wi = initial angular velocity when person is at center = 0.95 rad/s

wf = final angular velocity when person is at edge = ?

Using conservation of angular momentum

(I + Ipi) wi = (I + Ipf) wf

(810 + 0) (0.95) = (810 + 575.91) wf

wf = 0.56 rad/s

KEi = initial rotational KE = (0.5) (I + Ipi) w2i = (0.5) (810 + 0) (0.95)2 = 365.51 J

KEf = initial rotational KE = (0.5) (I + Ipf) w2f = (0.5) (810 + 575.91) (0.56)2 = 217.31 J

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