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A force is applied to the rim of a disk that can rotate like a merry-go-round, so as to change its angular velocity. Its initial and final angular velocities, respectively, for four situations are: (a) -2 rad/s, 5 rad/s; (b) 2 rad/s, 5 rad/s; (c) -2 rad/s, -5 rad/s; and (d) 2 rad/s, -5 rad/s. Rank the situations according to the work done by the torque due to the force, greatest first.

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Answer

from work energy theorem we can say that work done is equal to change in kinetic energy.

 [tex]W = \Delta KE = I\omega_f^2 - I\omega_i^2[/tex]

now, we have given four choices where initial and final angular speed are given

square of 2 and -2 is equal to 4

square of 5 and -5 is equal to 5

By inserting all the given option.

[tex]W = I(5^2-(-2)^2)[/tex]

       W = 21I J

Hence, in all the option the result will be same because magnitude of each option is same.

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