Question

The rotor in a centrifuge has an initial angular speed of 430 rad/s. After 4.1 s of constant angular acceleration, its angular speed has increased to 540 rad/s.During this time, what was the angular acceleration of the rotor?

Answer 1

The angular acceleration of the rotor is approximately 26.83 rad/s², calculated using the change in angular speed divided by the time over which the change occurred.

Step-by-step explanation:

The student has asked about calculating the angular acceleration of a rotor in a centrifuge. This involves applying principles of rotational motion from physics.

To find the angular acceleration, we use the formula α = (ωf - ωi) / t, where α is the angular acceleration, ωf is the final angular velocity, ωi is the initial angular velocity, and t is the time duration involved.

Let's apply this formula:

Initial angular speed, ωi = 430 rad/s

Final angular speed, ωf = 540 rad/s

Time, t = 4.1 s

Plugging these values into the formula:

α = (540 rad/s - 430 rad/s) / 4.1 s

α = 110 rad/s / 4.1 s

α = 26.83 rad/s² (rounded to two decimal places)

Therefore, the angular acceleration of the rotor is approximately 26.83 rad/s².