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.

This question can be solved by using the equations of motion in angular form.

A) Angular acceleration of the centrifuge is "52.63 rad/s²".

B) Angular Displacement is "4749.9 rad".

A)

To find the angular acceleration we will use the first equation of motion:

where,

= angular acceleration = ?

t = time interval = 9.5 s

= final angular sped = 750 rad/s

= initial angular speed = 250 rad/s

Therefore,

α = 52.63 rad/s²

B)

To find angular displacement we will use the second equation of motion:

θ = 4749.9 rad

Learn more about the angular motion here:

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The attached picture shows the angular equations of motion.

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

increasing transnational kinetic energy. because the transnational kinetic energy formula consists of only two variables, mass and velocity, increasing one of those properties is the only way to increase an object's transnational kinetic energy. increases to mass and velocity, however, do not have the same impact.