How do I find tangential acceleration?

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To find tangential acceleration, calculate the change in speed over time as the centrifuge spins up. Given that it takes 1 minute and 14 seconds to reach the maximum speed of 15,180 revolutions per minute, first convert this speed into meters per second. Use the formula for tangential acceleration, which is the change in velocity divided by the time taken for that change. The discussion emphasizes understanding the relationship between tangential acceleration and the rate of change of speed during the centrifuge's acceleration phase. Proper implementation of these calculations will yield the desired tangential acceleration value.
Loppyfoot
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Homework Statement


You are designing a centrifuge to spin at a rate of 15,180 rev/min.
(a) Calculate the maximum centripetal acceleration that a test-tube sample held in the centrifuge arm 15.2 cm from the rotation axis must withstand.
I found (a) by the formula v2/r and got approximately 382111m/s2 for the centripetal acceleration.

(b) It takes 1 min, 14 s for the centrifuge to spin up to its maximum rate of revolution from rest. Calculate the magnitude of the tangential acceleration of the centrifuge while it is spinning up, assuming that the tangential acceleration is constant.

How do I find the tangential acceleration? I know that it is dv/dt, but how do I implement this equation into the problem?

Thanks
 
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(a) looks good.

Tangential acceleration is the rate of change of speed .
 
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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