Speed of Rotation to Experience X Acceleration

In summary, the problem requires finding the necessary rpm for a centrifuge in order for a particle to experience an acceleration of 115,000 g's at a distance of 9.00cm from the axis of rotation. After converting the g's to m/s^2 and the radius to 0.09m, the equation v=(square root)(ar) is used to solve for the velocity. Then, the angular velocity is found using the equation v = rw and finally converted to rpm.
  • #1
Hisui
8
0

Homework Statement



How fast (in rpm) must a centrifuge rotate if a particle 9.00cm from the axis of rotation is to experience an acceleration of 115,000 g's?

Homework Equations



Either v=2(pi)r/T or v=(square root)(ar) ...not knowing which of these to use is possibly my first problem...

The Attempt at a Solution



First, I converted the g's to m/s^2 and got 11,734.7m/s^2 and the radius to 0.09m... I tried solving for v with both equations above and (obviously) got two completely different answers... my notes make it look like my professor was using both, but surely for different things...?

Also, I can't seem to be able to convert this into rpm... I got the circumference to be 0.57m, so I tried to use that as one rotation, then tried using v=2(pi)r/T where T is 60s (I figured this would make it rpm)... but that gave me 0.0095m/s... which left me again with trying to figure out how to convert it into rpm... but I still don't think that's right, because the actual answer is supposed to be 3.38 x 10^4 rpm...
 
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  • #2
"v=(square root)(ar)" (you can't use the other equation because you don't know T... T is not 60)

solve for v here... remember to convert r to m.

then find the angular velocity. v = rw where w is angular velocity.

then convert to rpm.
 
  • #3


I would first clarify with my professor which equation to use for this problem and in what context. The two equations mentioned, v=2(pi)r/T and v=(square root)(ar), have different applications and it is important to use the correct one in order to obtain the correct answer.

Assuming that the correct equation to use is v=(square root)(ar), I would proceed with the following solution:

Given:
Acceleration (a) = 11,734.7 m/s^2
Radius (r) = 0.09 m

To find:
Speed (v) in rpm

Solution:
1. Convert the acceleration from m/s^2 to cm/s^2:
a = 11,734.7 m/s^2 x (100 cm/1 m)^2 = 1.17347 x 10^9 cm/s^2

2. Use the equation v=(square root)(ar) to solve for v:
v = (square root)(a x r)
v = (square root)(1.17347 x 10^9 cm/s^2 x 0.09 m)
v = 3.38 x 10^4 cm/s

3. Convert the speed from cm/s to m/s:
v = 3.38 x 10^4 cm/s x (1 m/100 cm) = 338 m/s

4. Convert the speed from m/s to rpm:
v = 338 m/s x (1 min/60 s) x (1 rev/0.57 m) = 3.38 x 10^4 rpm

Therefore, the centrifuge must rotate at a speed of 3.38 x 10^4 rpm in order for the particle 9.00 cm from the axis of rotation to experience an acceleration of 115,000 g's.
 

1. What is the relationship between speed of rotation and acceleration?

The speed of rotation and acceleration are directly related. As the speed of rotation increases, the acceleration also increases.

2. How does the speed of rotation affect the experience of acceleration?

The higher the speed of rotation, the greater the experience of acceleration. This is because the faster the object is rotating, the faster it is changing direction and experiencing changes in velocity, which is what we perceive as acceleration.

3. Is there a limit to how fast an object can rotate before the acceleration becomes too intense?

Yes, there is a limit to how fast an object can rotate before the acceleration becomes too intense. This limit is determined by various factors such as the material and structure of the object, as well as the physical limitations of the human body.

4. Can the speed of rotation be used to control the intensity of acceleration experienced?

Yes, the speed of rotation can be used to control the intensity of acceleration experienced. By adjusting the speed of rotation, we can increase or decrease the acceleration experienced by an object.

5. Are there any real-world applications for understanding the relationship between speed of rotation and acceleration?

Yes, there are many real-world applications for understanding the relationship between speed of rotation and acceleration. This knowledge is essential in fields such as engineering, sports science, and transportation, where precise control of acceleration is necessary for optimal performance and safety.

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