## At its lowest setting a centrifuge rotates with an angular speed of ω1 = 250 rad/s. When it is switched to the next higher setting it takes

Question

At its lowest setting a centrifuge rotates with an angular speed of ω1 = 250 rad/s. When it is switched to the next higher setting it takes t = 9.5 s to uniformly accelerate to its final angular speed ω2 = 750 rad/s.

A) Calculate the angular acceleration of the centrifuge α1 in rad/s2 over the time interval t.

B) Calculate the total angular displacement (in radians) of the centrifuge, Δθ, as it accelerates from the initial to the final speed.

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5 months 2021-08-31T06:49:34+00:00 1 Answers 12 views 0

Part(a): The angular acceleration is .

Part(b): The angular displacement is .

Explanation:

Part(a):

If be the initial angular speed, final angular speed and angular acceleration  of the centrifuge respectively, then from rotational kinematic equation, we can write where ‘ ‘ is the time taken by the centrifuge to increase its angular speed.

Given, , and . From equation ( ), the angular acceleration is given by Part(b):

Also the angular displacement ( ) can be written as 