Solving Rotational Speed Homework with Radius of 40cm

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The discussion focuses on calculating the rotational speed of a tire with a radius of 40 cm spinning at 2500 revolutions per minute (rev/min). The formula used is w = v/r, where the user initially calculates w as 62.5 radians per second. There is confusion regarding the distinction between rotational speed and linear velocity, with participants clarifying that rev/sec is the correct measure for rotational speed. The conversation emphasizes the importance of understanding the units involved in the calculations. Accurate interpretation of these concepts is crucial for solving similar physics problems effectively.
zombie4000
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Homework Statement


Tire with a radius of 40cm spinning at 2500 rev/min. What is the rotational speed?


Homework Equations


w=v/r
w=2500revmin/40cm
w=62.5 rad/sec

Does that sound right? I am confused
 
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Er... rev/min is a rotational speed.

Im not too sure what you are trying to work out.
 
Okay. Thats the exact problem I have on my sheet. I asked a few others and they said that the rev/sec is the rotational speed.
 
Look at your formula, and look at the units involved.

That will find a linear velocity at the outer edge of that ball, not rotational.
 
Thanks for the help!
 
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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