Angular Acceleration of a centrifuge

In summary, when the centrifuge is switched off, it rotates 48 times before coming to a stop. The centrifuge has an angular acceleration of -420 rad/s^2.
  • #1
vipertongn
98
0
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.

Relevent 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
 
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  • #2
Last edited:
  • #3
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
 
Last edited:
  • #4
vipertongn said:
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.
 
  • #5
i edited my last post, is that correctly calculated?
 
  • #6
vipertongn said:
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.)
 
  • #7
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?
 
  • #8
vipertongn said:
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.

ωf2 = ωi2 + 2*α*θ

But they give you revolutions. And there are 2π radians in a revolution and θ is in radians.
 
  • #9
ohhhh i see now, thanks lowly ^^
 
  • #10
Remember the acceleration α they want is (-) because you are slowing down to a stop.
 

Related to Angular Acceleration of a centrifuge

1. What is angular acceleration?

Angular acceleration refers to the rate of change of angular velocity of an object. It is a measure of how quickly the object's rotational speed is changing.

2. How is angular acceleration calculated?

Angular acceleration can be calculated by dividing the change in angular velocity by the change in time. The formula is angular acceleration = (final angular velocity - initial angular velocity) / time.

3. How does a centrifuge use angular acceleration?

A centrifuge uses angular acceleration to separate substances of different densities by spinning them at high speeds. This causes the substances to experience different centrifugal forces, allowing them to be separated.

4. What factors affect the angular acceleration of a centrifuge?

The angular acceleration of a centrifuge is affected by the radius of rotation, angular velocity, and the mass of the substances being separated. The larger the radius and/or angular velocity, the greater the angular acceleration will be. Similarly, the greater the mass of the substances, the lower the angular acceleration will be.

5. How is angular acceleration related to centripetal acceleration?

Angular acceleration is directly related to centripetal acceleration, as both are measures of the rotational motion of an object. Centripetal acceleration is the linear acceleration towards the center of rotation, while angular acceleration is the rotational acceleration in radians per second squared.

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