Uniform angular acceleration - degrees per second?

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A wheel with uniform angular acceleration starts from rest and rotates 88.6 degrees in the first second. The discussion focuses on calculating the angles rotated in subsequent seconds, emphasizing that the angular acceleration is constant. The calculated angular acceleration is 1.546 radians/sec², but confusion arises regarding the angles for the second and third seconds. It's noted that the angle rotated in the second second should exceed 88.6 degrees due to increasing speed. The conversation highlights the importance of using the correct equations for rotational motion to find the solution.
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Homework Statement



A wheel is subjected to uniform angular acceleration. Initially its angular velocity is zero. During the first 1-s time interval, it rotates through an angle of 88.6degrees.

(a) Through what angle does it rotate during the next 1-s time interval?
(b) Through what angle during the third 1-s time interval?

Homework Equations



a = (wf - wi)/(tf-ti)
360 degrees = 2*pi*radians

The Attempt at a Solution



i found a = 1.546, where do i go from here?
 
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okay, i came up with 132.87 degrees using one of the equations, do i subtract 88.6 degrees (the original rotation?)
 
i am so confused, and everything i try is wrong
 
Yes, assuming you have calculated the angle turned in 2 secs. It's not very helpful to say "using one of the equations". But I think you are wrong because I'd expect more turn in the second period than the first ( because the speed is increasing linearly).
 
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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