How fast (in rpm ) must a centrifuge rotate if a particle 8.00 from the axis of rotation is to experience an acceleration of 117000g's?
Well. What is it
To determine the required rotational speed (in rpm) for a centrifuge to provide a specific acceleration to a particle, we need to use the formula for centrifugal acceleration:
acceleration = (angular velocity)^2 * radius
Here, the acceleration is given as 117,000g's, and the particle is located at a distance of 8.00 cm from the axis of rotation. We need to convert the distance to meters, and the acceleration from g's to m/s^2.
1 g = 9.8 m/s^2 (acceleration due to gravity)
Converting the distance:
8.00 cm = 8.00 / 100 = 0.08 meters
Converting the acceleration:
117,000 g's = 117,000 * 9.8 m/s^2 = 1,146,600 m/s^2
Now, let's rearrange the formula to solve for angular velocity:
angular velocity = sqrt(acceleration / radius)
Plugging in the values:
angular velocity = sqrt(1,146,600 m/s^2 / 0.08 m) = sqrt(14,332,500) m/s
Finally, to convert angular velocity to rpm (revolutions per minute), we need to multiply it by the conversion factor:
1 revolution = 2π radians
angular velocity (in rpm) = sqrt(14,332,500) m/s * (1 revolution / 2π radians) * (60 seconds / 1 minute)
Calculating this value:
angular velocity (in rpm) = sqrt(14,332,500) * (60 / 2π) ≈ 32,206 rpm
Therefore, the centrifuge must rotate at approximately 32,206 rpm for a particle situated 8.00 cm from the axis of rotation to experience an acceleration of 117,000g's.