Calculating Linear Speed of Test Tube in Centrifuge

In summary, the formula for calculating linear speed of a test tube in a centrifuge is v = rω. To convert from radians per second to revolutions per minute, multiply the angular velocity by 60/(2π) or approximately 9.55. This formula can be used to calculate the linear speed of any object in circular motion, as long as the units are consistent. Linear speed and angular velocity are directly proportional, with a direct relationship described by the formula v = rω. As the radius of rotation increases, the linear speed in a centrifuge also increases due to the direct relationship between v and r.
  • #1
mwegimont
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Homework Statement



Find the linear speed of the bottom of a test tube in a centrifuge if the centripetal acceleration there is 5.3×104 times the acceleration of gravity. The distance from the axis of rotation to the bottom of the test tube is 7.3 .

Homework Equations




I have gotten answers of 1900 and 223 m/s.I cannot figure out how to do this problem
 
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  • #2
Show how you arrived at those answers. What are the units for the distance? What's the formula for centripetal acceleration?
 

1. What is the formula for calculating linear speed of a test tube in a centrifuge?

The formula for calculating linear speed of a test tube in a centrifuge is v = rω, where v is the linear speed, r is the radius of rotation, and ω is the angular velocity.

2. How do I convert the angular velocity from radians per second to revolutions per minute?

To convert from radians per second to revolutions per minute, multiply the angular velocity by 60/(2π) or approximately 9.55.

3. Can I use the same formula to calculate the linear speed of any object in circular motion?

Yes, the formula v = rω can be used to calculate the linear speed of any object in circular motion, as long as the units are consistent (e.g. using meters for r and radians per second for ω).

4. What is the relationship between linear speed and angular velocity?

Linear speed and angular velocity are directly proportional, meaning that as one increases, the other also increases. This relationship is described by the formula v = rω, where v is the linear speed, r is the radius of rotation, and ω is the angular velocity.

5. How does changing the radius of rotation affect the linear speed in a centrifuge?

As the radius of rotation increases, the linear speed in a centrifuge also increases. This is because the formula for linear speed, v = rω, shows a direct relationship between v and r. Therefore, a larger r will result in a larger v.

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