A cockroach of mass m lies on the rim of a uniform disk of mass 8.00 m that can rotate freely about its center like a merry-go-round. Initially the cockroach and disk rotate together with an angular velocity of 0.229 rad/s. Then the cockroach walks halfway to the center of the disk. (a) What then is the angular velocity of the cockroach-disk system? (b) What is the ratio K/K0 of the new kinetic energy of the system to its initial kinetic energy?
(Please be clear)
a)
I11 = I22
(0.5 * 8m * r2 + m* r2) * 0.229 = (0.5 * 8m * r2 + m * (r/2)2) 2
(5 mr2) * 0.229 = (4.25 mr2) * 2
2= 1.145 / 4.25 = 0.269 rad/s
The angular velocity of the cockroach-disk system = 0.269 rad/s
b)
K / Ko = I222 / I112 = (4.25 mr2 * 0.2692) / (5 mr2* 0.2292 ) = 1.17
The ratio K/K0 of the new kinetic energy of the system to its initial kinetic energy = 1.17
A cockroach of mass m lies on the rim of a uniform disk of mass 8.00...
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