Find the acceleration at 4000rpm

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To find the acceleration at the end of a test tube in a centrifuge rotating at 4000 rpm, the relevant equation is a = rω², where 'a' is acceleration, 'r' is the radius (10 cm in this case), and 'ω' is the angular velocity in radians per second. First, convert 4000 rpm to radians per second by using the conversion factor (2π radians per revolution). The acceleration can then be calculated by substituting the values into the equation. Understanding circular motion principles is essential for this problem, and consulting a textbook on the topic can provide further examples and clarification. Proper application of the formula will yield the required acceleration value.
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Homework Statement


A typical laboratory centrifuge rotates at 4000 rpm. Test tubes have to be placed into a centrifuge very carefully because of the very large accelerations.What is the acceleration at the end of a test tube that is 10 cm from the axis of rotation?

Homework Equations


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The Attempt at a Solution


I know that the 10cm we are given isn't a radius, so i have no idea where we are to start.
 
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If you're in school, and have a textbook, i would suggest looking into Circular Motion and Gravitation, my textbook even has an example of the question your asking.
 
In not at school, my textbook doesn't have an example of it, i just need an equation for the work.
 
Your textbook would have an example. Your probably not looking in the right place. I'll give you a jumpstart. You need this equation to solve it. a=rw^2. you should be able to figure the rest out.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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