Final answer:
To determine the average angular acceleration of a centrifuge rotor accelerated from 20,000 rpm to a final speed in 30 seconds, use the formula (final angular velocity - initial angular velocity) / time. Convert the speeds to rad/s using the conversion factor 1 rev = 2π rad.
Step-by-step explanation:
To determine the average angular acceleration of a centrifuge rotor, we can use the formula:
Angular acceleration (α) = (final angular velocity - initial angular velocity) / time
Given that the rotor is accelerated from 20,000 rpm to a final speed in 30 seconds, we need to convert the speeds to rad/s. Using the conversion factor: 1 rev = 2π rad, we can calculate:
Initial angular velocity = 20,000 rpm x 2π rad/1 rev x 1 min/60 s = (20,000 x 2π) / 60 rad/s
Final angular velocity = Final speed x 2π rad/1 rev x 1 min/60 s = (Final speed x 2π) / 60 rad/s
Substituting the values into the formula, and assuming the final speed is given in rpm:
Angular acceleration (α) = ((Final speed x 2π) / 60 rad/s - (20,000 x 2π) / 60 rad/s) / 30 s
Calculate the angular acceleration using this formula to find the average angular acceleration of the centrifuge rotor.