Angular Acceleration of a centrifuge

[vipertongn]

A centrifuge in a medical laboratory rotates at an angular speed of 3400 rev/min. When switched off, it rotates 48.0 times before coming to rest. Find the constant angular acceleration of the centrifuge.

relevant equations: ωf = ωi + αt

My work:
I found out the time by (48 rev)(1min/3400 rev)(60 sec/min) = 0.847 seconds

I then converted the rev/min to rad/sec (3400 rev/min)(2pi/1rev)(1min/60sec)= 356 rad/sec

So I set the problem up like 0=356 rad/sec + α(0.847 seconds)
-356/0.847=α
α = -420 rad/s^2

 

[LowlyPion]

Not quite.

You don't know a or t.

Consider how the angular kinematic equations compare to the linear kinematic equations:
http://hyperphysics.phy-astr.gsu.edu/hbase/mi.html#rlin

In particular the Vf² = Vi² + 2a*x analog in rotational terms.

 

[vipertongn]

yes but couldn't you find time using the equation i did earlier? I'm trying to solve for a tho...

However, if I were to calculate what you put in...

0=3400 rev/min+2a(48rev)
-3400/96=a
a=-35 min^-1

 

[LowlyPion]

yes but couldn't you find time using the equation i did earlier? I'm trying to solve for a tho...

Yes. You can use that equation for time, once you've found the α based on the θ given and the initial ω.

 

[vipertongn]

i edited my last post, is that correctly calculated?

 

[LowlyPion]

i edited my last post, is that correctly calculated?

Well I left an exponent out of my earlier post and I corrected that apparently after you used it.

Instead of blindly using formulas, I encourage you to review the link and think about how the rotational kinematic equations relate to the regular one dimensional kinematics that I think you already know.

But that aside (and the exponent of the initial ω corrected) your calculation hasn't accounted for the conversion from min to sec. (Unless you don't need your answer in sec.)

 

[vipertongn]

if i put it in seconds it ends up being 0.583 s^-1 but that' can't be the acceleration...shouldn't it be to the -2?

 

[LowlyPion]

if i put it in seconds it ends up being 0.583 s^-1 but that' can't be the acceleration...shouldn't it be to the -2?

Look you need to understand the equations.

ω_f² = ω_i² + 2*α*θ

But they give you revolutions. And there are 2π radians in a revolution and θ is in radians.

 

[vipertongn]

ohhhh i see now, thanks lowly ^^

 

[LowlyPion]

Remember the acceleration α they want is (-) because you are slowing down to a stop.