A person of mass 75 kg stands at the center of a rotating merry-go-round platfor

Question

A person of mass 75 kg stands at the center of a rotating merry-go-round platform of radius 3.2 m and moment of inertia 1100 kg·m2. The platform rotates without friction with angular velocity 1.5 rad/s. The person walks radially to the edge of the platform.

(a) Calculate the angular velocity when the person reaches the edge in rad/s.

(b) Calculate the rotational kinetic energy of the system of platform plus person before and after the person's walk in joules.

have been working on this problem for so long with no luck.

Explanation / Answer

a) using angular momentum(I) conservation ,

(1100 + 0 ) x 1.5 = (1100 + 75 x 3.22 ) x

= 0.883 rad/s

b) before person walk : K.E. = I2 /2   = (1100 + 0 ) x 1.52 /2   = 1237.5 J

after : K.E. = (1100 + 75 x 3.22 ) x 0.8832 /2 = 728.23 J

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