To find the average angular acceleration of the centrifuge rotor, we need to determine the change in angular velocity and the time taken.
Given: Initial angular velocity, ω₀ = 0 (since the rotor is at rest) Final angular velocity, ω = 20,000 rpm Time, t = 30 seconds
First, we need to convert the final angular velocity from rpm (revolutions per minute) to rad/s (radians per second) since the unit of angular acceleration is rad/s².
1 revolution = 2π radians 1 minute = 60 seconds
Final angular velocity, ω = 20,000 rpm ω = 20,000 * (2π/60) rad/s ω ≈ 2094.4 rad/s
Next, we can calculate the average angular acceleration using the formula:
Average angular acceleration (α) = (ω - ω₀) / t
Substituting the values:
Average angular acceleration (α) = (2094.4 rad/s - 0) / 30 s α ≈ 69.8 rad/s²
Therefore, the average angular acceleration of the centrifuge rotor is approximately 69.8 rad/s².