How fast (in rpm) must a centrifuge rotate if a particle 8.2 cm from the axis of rotation is to experience an acceleration of 200000 g 's?

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What is the APY for money invested at each rate? (A) 6% compounded monthly (B) 4% compoumded continuously

11089.10

To determine the speed (in rpm) at which a centrifuge must rotate for a particle at a certain distance from the axis to experience a desired acceleration, we can use the following formula:

Acceleration = (Angular velocity)^2 x radius

Where:
- Acceleration is given in terms of "g's." In this case, it's 200,000 g's.
- Angular velocity is the rotational speed of the centrifuge, expressed in radians per second (rad/s).
- Radius is the distance of the particle from the axis of rotation, given as 8.2 cm.

First, let's convert the radius from centimeters to meters:
Radius = 8.2 cm = 0.082 m

Next, we need to convert the desired acceleration from g's to m/s^2. 1 g is equal to the acceleration due to gravity, approximately 9.8 m/s^2.
Acceleration = 200,000 g's x 9.8 m/s^2/g = 1,960,000 m/s^2

Now, we can solve the equation for angular velocity:
1,960,000 m/s^2 = (Angular velocity)^2 x 0.082 m

Divide both sides of the equation by 0.082 m:
(Angular velocity)^2 = (1,960,000 m/s^2) / 0.082 m
(Angular velocity)^2 = 23,902,439,024.39

Take the square root of both sides to solve for angular velocity:
Angular velocity = √23,902,439,024.39
Angular velocity ≈ 154,717.45 rad/s

Finally, we can convert the angular velocity to revolutions per minute (rpm):
1 revolution = 2π radians
1 minute = 60 seconds

Angular velocity in rpm = (154,717.45 rad/s) x (1 revolution / 2π radians) x (60 seconds / 1 minute)
Angular velocity in rpm ≈ 1,473,058.28 rpm

Therefore, the centrifuge must rotate at approximately 1,473,058.28 rpm for the particle at 8.2 cm from the axis to experience an acceleration of 200,000 g's.