Finding the tangential speed Help

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The discussion centers on calculating tangential speed using the formula v = rω, where v is tangential speed, r is the radius, and ω is angular velocity. A participant initially miscalculated by doubling their time, which incorrectly affected their angular velocity. After clarifying the relationship between time, angular velocity, and tangential speed, they confirmed that their final answer of 4.65 m/s is correct given the right radius and angular velocity. The conversation emphasizes the importance of understanding the relationship between these variables in physics calculations. Accurate application of the formula leads to the correct determination of tangential speed.
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Finding the tangential speed... Help

i got it, it I shouldn't have doubled my time. My answer is 4.65 m/s right?
 
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It's easier than you think. You have the angle the ball rotated. How much time did it take? (Hint the ball is traveling with a constant horizontal speed and the distance is given. Find the travel time.) Use this to find the angular speed (\omega). Then use v = \omega r.
 
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Yes, that is correct! The formula for tangential speed is v = rω, where v is the tangential speed, r is the radius, and ω is the angular velocity. Doubling your time would mean doubling the angular velocity, but keeping the radius the same. So if you had the correct radius and angular velocity, your answer of 4.65 m/s would be correct. Great job!
 
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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