Angular Deceleration Calculation for Medical Lab Centrifuge

[ScienceGirl90]

Homework Statement

A medical laboratory centrifuge is rotating at 377 rad/s (3600 rpm). When it is switched off, it rotates 78 times before it comes to rest. Assuming constant angular deceleration, what is the angular deceleration?

Homework Equations

w=at+w_(initial)

The Attempt at a Solution

I'm confused as to what is my initial and final angular velocity and how to generally solve the problem with the info provided. My first thought was to make 377 rad/s be my initial velocity and 78 rad/s be the final velocity but I don't think that's right...

 

[tiny-tim]

Hi ScienceGirl90!

You know the initial angular speed, the final angular speed (zero), and the total angular distance, but not the time …

so use one of the other standard constant acceleration equations.

 

[ScienceGirl90]

Oh ok! So then 78 rotations is the distance then?

 

[tiny-tim]

(just got up :zzz: …)

Yup!

 

[rwisz]

I would approach this problem by first defining the variables and understanding the given information. In this case, we know the initial angular velocity of the centrifuge, which is 377 rad/s, and the final angular velocity, which is 0 rad/s (since it comes to rest). We also know the number of rotations it takes for the centrifuge to decelerate, which is 78.

Next, I would use the formula for angular acceleration, which is alpha = (w(final) - w(initial))/t. In this case, we know the initial and final angular velocities, so we just need to find the time it takes for the centrifuge to decelerate. This can be calculated by dividing the number of rotations (78) by the initial angular velocity (377 rad/s). This gives us a time of approximately 0.207 seconds.

Plugging in the values, we get alpha = (0-377 rad/s)/(0.207 s) = -1822.71 rad/s^2. Therefore, the angular deceleration of the centrifuge is approximately -1822.71 rad/s^2.

It is important to note that this is a negative value, indicating that the centrifuge is decelerating in the opposite direction of its initial rotation. This is expected since the centrifuge is coming to a stop.

In conclusion, the angular deceleration of the medical laboratory centrifuge is -1822.71 rad/s^2.