Find Angular Velocity of Centrifuge with Particle 10.0 cm Away

In summary, the formula for finding the angular velocity of a centrifuge with a particle 10.0 cm away is: angular velocity = (2 * π * radius) / time. The radius can be determined by measuring the distance between the center of rotation and the particle. The unit for time in the formula is seconds (s). To convert the angular velocity to RPM, the formula is RPM = (angular velocity * 60) / (2 * π). This formula can be used for any centrifuge as long as the distance of the particle from the center of rotation is known.
  • #1
Miike012
1,009
0
A centrifuge is used to increase the sedimentation rate of
particles suspended in a liquid, over the rate produced
by gravity alone. Find the angular velocity of a centri -
fuge in which a particle 10.0 cm from the axis of rotation
experiences a radial acceleration of 1.00* 10^3
times gravitational acceleration g.

Solution: radius (r) = 0.01 m ; ar = 1.00*10^3*9.80


1.00*10^3*9.80 = (.01)w^2

w = ( 1.00*10^3*9.80/.01)^(1/2) = 989

Answer is 313 rad/sec...

where did I go wrong>?
 
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  • #2
10.0 cm = 0.1 m

Do not underestimate the girth of the centimeter.
 
  • #3
thank you,
 

1. What is the formula for finding the angular velocity of a centrifuge with a particle 10.0 cm away?

The formula for finding the angular velocity of a centrifuge with a particle 10.0 cm away is: angular velocity = (2 * π * radius) / time, where radius is the distance of the particle from the center of rotation and time is the time taken for one complete rotation.

2. How do I determine the radius in the formula for finding the angular velocity?

You can determine the radius by measuring the distance between the center of rotation and the particle. In this case, the radius would be 10.0 cm.

3. What unit should be used for the time in the formula?

The unit for time in the formula is seconds (s). This is the standard unit for measuring time in the International System of Units (SI).

4. How do I convert the angular velocity to revolutions per minute (RPM)?

To convert the angular velocity to RPM, you can use the formula: RPM = (angular velocity * 60) / (2 * π). This will give you the number of revolutions per minute.

5. Can I use this formula for finding the angular velocity of any centrifuge?

Yes, this formula can be used for finding the angular velocity of any centrifuge, as long as the distance of the particle from the center of rotation is known.

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