If a centrifuge rotates at an angular speed of 3,600 rev/min. What constant angular acceleration?

Question

A centrifuge in a medical laboratory rotates at an angular speed fo 3,600 rev/min. When switched off, it rotates throught 50.0 revolutions before coming to rest. Find the constant angularr acceleratioin of the centrifuge?

COULD SOMEONE PLEASE HELP ME ON THIS PROBLEM. I TRIED WORKING IT OUT, BUT MY ANSWER IS DIFFERENT FROM THE BOOK. PLEASE SHOW ME THE RIGHT WAY AND THE ANSWER. THANK YOU

Answer 1

initial speed = 3600 rev /min , Final speed = 0

convert 3600 rev / min to rad/s unit

= 3600 rev /min x (2 pi / 1 rad ) x ( 1 min/ 60 sec ) is about

3.77 x 10^2 rad/s

also change beta total = 50 rev to rad = 50 rev x 2pi =3.14 x

10^2 rad = beta total

then use the constant acceleration formula which is not involving t in the equation that is

Vf^2 = Vi^2 + 2a (beta total)

now u can algrebriaclly solving for "a" then after that putting the value which we convert into the equation to get final answer.

the acceleration should be negative coz the centrifuge tends to stop

also change letter V and a to the Greek letter = omega and alpha too.

Answer 2

It's not necessary to switch to radians unless some radius R and/or circumference C is in the equations. Or unless you need the answer in radians. Then you need to use the 2pi/rev conversion for unit consistency.

From the linear equivalent, v^2 = v0^2 + 2aS, we can write the angular version w^2 = w0^2 + 2 alpha N; where w = 0 the end angular velocity, w0 = 3,600 rpm the initial angular velocity, alpha is the angluar acceleration (in rev/min^2) you are looking for, and N = 50 is the distance traveled in number of revolutions.

Thus, alpha = w0^2/2N in revolutions per min^2; where w0 = 3,600 rpm and N = 50 revs. And there you have it, alpha, the acceleration (deceleration) but in rev/min^2 rather than radians/min^2.

I bring this up because some of your answerers claim you have to change to radians to work this problem. As you can see, you do not...unless you want the answer in radians. For that, just multiply the alpha * 2 pi and you have the answer in radians/min^2. Or, if you want alpha in rad/sec^2, you also need to convert the minutes into seconds for the angular velocity.

My guess, you have the right answer already, but in rev/min^2; not in radians/min^2 or radian/sec^2, whichever the book is looking for. Try multiplying what you already did by 2 pi and see what you get. If that doesn't do it, convert the minutes into seconds for the angular velocity as well.