Gymnast's Floor Routine: Angular Velocity & Time

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A gymnast's floor routine involves a tumbling run where she increases her angular velocity from 3.00 to 4.65 revolutions per second while completing half a revolution. To calculate the time taken for this maneuver, one must apply kinematic equations relevant to rotational motion. The term "one-half of a revolution" corresponds to an angle of 180 degrees or π radians. Understanding this angle is crucial for determining the time required for the gymnast's spin. The discussion emphasizes the importance of kinematic principles in solving problems related to angular motion.
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A gymnast is performing a floor routine. In a tumbling run she spins through the air, increasing her angular velocity from 3.00 to 4.65 rev/s while rotating through one-half of a revolution. How much time does this maneuver take?

ok I understand that I am going to be using one of the equations of kinematics for rotational and linear motion. I just don't understand what I am suspose to use the "one-half of a revolution" for.
 
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What angle is one half of a revolution?
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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