How do I find tangential acceleration?

[Loppyfoot]

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

 

[Redbelly98]

(a) looks good.

Tangential acceleration is the rate of change of speed .

 

[tomcue]

for your question! In order to find the tangential acceleration, you can use the formula a = rω^2, where r is the distance from the rotation axis and ω is the angular velocity (in radians per second). This formula is derived from the relationship between linear and angular velocity, v = rω, and the definition of acceleration, a = dv/dt. So, to implement this equation into the problem, you would first need to convert the angular velocity of 15,180 rev/min to radians per second (multiply by 2π/60), and then plug it into the formula along with the given distance of 15.2 cm. This will give you the magnitude of the tangential acceleration while the centrifuge is spinning at its maximum rate.

To find the tangential acceleration while the centrifuge is spinning up from rest, you can use the equation a = Δv/Δt, where Δv is the change in velocity and Δt is the change in time. In this case, you would need to calculate the change in angular velocity from 0 to 15,180 rev/min and the corresponding change in time of 1 min and 14 seconds. Then, plug these values into the equation to find the magnitude of the tangential acceleration during the spinning up process.

I hope this helps! Let me know if you have any further questions.