How Can I Solve These Rotational Kinematics Problems?

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The discussion centers on solving two rotational kinematics problems involving angular acceleration and displacement. The first problem involves a spinning wheel with an angular acceleration of -4.00 rad/s², changing its angular velocity to -25.0 rad/s over a time period, which is calculated to be 12.5 seconds. The second problem concerns a fan blade with a constant angular acceleration of 2.00 rad/s² that rotates through 285 radians in 11.0 seconds, with the time taken to reach the start of this interval determined to be 7.45 seconds. Participants emphasize the importance of understanding the concepts of negative acceleration, angular displacement, and the relationship between revolutions and radians. The discussion highlights the need for detailed guidance rather than complete solutions to foster comprehension.
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Rotational Kinematics HELP!?

I desperately need help with two rotational kinematics problems. I do not know what to do in both cases. If someone could be kind enough to go through a solution for me to see it would be very helpful in understanding the problem. Please try and be detailed in your answer as I really want to understand how it is solved.

Homework Statement

1) A spinning wheel on a fireworks display is initially rotating in a counterclockwise direction. The wheel has an angular acceleration of -4.00rad/s2. Because of this acceleration, the angular velocity of the wheel changes from its initial value to a final value of -25.0rad/s. While this change occurs, the angular displacement of the wheel is zero. Find the time required for the change in the angular velocity to occur.
Answer: 12.5s

2) A fan blade whose angular acceleration is a constant 2.00 rad/s^2 rotates through an angle of 285 radians in 11.0s. How long did it take the blade starting from rest to reach the beginning of the 11.0s interval?
Answer: 7.45s

Homework Equations


Newtonian rotatational formulae.

The Attempt at a Solution


no idea i did the last 20 problems no problems but these 2 are stumping me.
 
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These hints should be enough:

1).negative acceleration means deceleration.
zero angular displacement means one complete revolution.
counter clockwise is positive direction.

2).2 pi radian = 1 revolution.
calculate the distance traversed in the desired time interval.
 
1) A spinning wheel on a fireworks display is initially rotating in a counterclockwise direction. The wheel has an angular acceleration of -4.00rad/s2. Because of this acceleration, the angular velocity of the wheel changes from its initial value to a final value of -25.0rad/s. While this change occurs, the angular displacement of the wheel is zero. Find the time required for the change in the angular velocity to occur.
Answer: 12.5s
I don't see how there's enough information there to answer the question. Specifically, what is the initial angular velocity?
 
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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