Calculating revolutions per minute

I have no idea why you did it.In summary, a centrifuge is a device used in medical laboratories to separate materials by rotating them at high speeds. To calculate the number of revolutions per minute a sample is making, the formula ac=(4pi^2r) / T^2 can be used. After rearranging the formula and solving for T, the correct answer is approximately 0.009 seconds for one revolution. However, this calculation may need to be re-evaluated for accuracy. Additionally, it is important to note that multiplying the period by 60 is not a correct way to calculate the revolutions per minute.
  • #1
Sosa

Homework Statement



A centrifuge is a device in which a small container of material is rotated at a high speed on a circular path. Such a device is used in medical laboratories, for instance, to cause the more dense red blood cells to settle through the less dense blood serum and collect at the bottom of the container. Suppose the centripetal acceleration of the sample is 4.60 x 10^3 times as large as the acceleration due to gravity. How many revolutions per minute is the sample making, if it is located at a radius of 4.59 cm from the axis of rotation?

Homework Equations


ac=(4pi^2r) / T^2

The Attempt at a Solution


rearranged the formula to get
T = sqrt (4pi^2r) / a
T = sqrt (4pi^2*0.0459) / 4.60 x 10^3 *9.8
T = 0.009358 *60 seconds
T = 0.561 rpm but it's wrong
 
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  • #2
Sosa said:
4.60 x 103 times as large
Or do you mean 103?
Where are your equations, and solution?
 
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  • #3
Asymptotic said:
Or do you mean 103?
Where are your equations, and solution?
updated it!
 
  • #4
Is T supposed to be the time in seconds for one revolution?
Re-evaluate the applicability of the formula you are using.
 
  • #5
First, check your calculation. I have done your calculation several times, in different ways, in case you, or your calculator, misinterpreted your badly-written (in terms of brackets) equation, and in no case did I get 0.009358 seconds. The correct (I think) answer is of the same order of magnitude, but not the same number.
Second, you don't multiply the period by 60 to get the rpm. Dimensional analysis should tell you that that's nonsense.
 

1. What is the formula for calculating revolutions per minute (RPM)?

The formula for calculating RPM is: RPM = (60 x f) / p, where f is the frequency in hertz and p is the number of poles in the motor.

2. How do I measure the frequency for calculating RPM?

The frequency can be measured using a tachometer, which is a device that measures the number of rotations per minute of a rotating object.

3. Can I calculate RPM without knowing the frequency?

No, the frequency is a crucial component in calculating RPM. Without knowing the frequency, it is not possible to accurately determine the RPM.

4. What units are used for RPM?

RPM is typically measured in revolutions per minute, but it can also be expressed in radians per second (rad/s) or revolutions per second (rps).

5. What factors can affect the accuracy of RPM calculations?

Several factors can affect the accuracy of RPM calculations, including changes in temperature, variations in load, and mechanical wear and tear on the rotating object.

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