Calculating Centrifugal Force 8

[jamesxi]

I am designing a unique gyroscopic/centrifugal machine, but know little about the calculations involved, so am hoping that someone here will be able to help.

Assume I have a 10cm radius centrifuge, and a 1kg mass at the end of the centrifuge, with the weight's center exactly at the 10cm mark. The centrifuge is spinning at 1,000 RPM. How would I calculate the centrifugal force (in kg) that such a system generates. I don't really need to factor in friction yet.

So, my variables are:
r(radius) = 10cm
m(mass) = 1kg
RPM = 1000
Cf(centrifugal force) = ?

Jimmy
jamesxi@yahoo.com

 

[Speedy]

Could someone explain the negative radius bit?

 

[cowski]

Thanks to FINN and Greg for setting me straight, maybe I should go design satellites for NASA or something!

 

[svanels]

radius is always positive Steven van Els
SAvanEls@cq-link.sr

 

[butelja]

svanels is correct. Think of a negative radius as a positive radius with a 180° phase shift.

 

[gearguru]

And force is allways a Newton or lbf.
Using word "weight" can be misleading, unless you say if it means mass or force. "kg of force" was used long time ago, some countries called it "kilopond" (I believe Germany) but because of the confusion it was replaced by Newton (1kgf = 9.81N)
gearguru

 

[jamesxi]

Its taking longer than I thought to get the full animation of my working machine, so I have a link to the non-working version that is somewhat similar. In this animation I only displayed the two main parts of the invention, so you can't see the structure that keeps the "thrusting arm" at a bearing of 90 degrees.

This machine is a centrifugal propulsion machine, which uses simple mechanical motion to generate centrifugal force meant to propel the machine. Keep in mind that this version does not work. It consists of a a centrifuge arm, a "thrusting" arm, and a "thrusting mass". The red line is only the path of the centrifuge. Looking at the invention I was at first thinking that it would be thrusted to the 90 degree mark using centrifugal force. But, I'm pretty sure that the center of the centrifuge has only been raised(correct me if I am wrong).

http://www.ultimateinteractive.com/images/animation2.gif

Fortunately their is a similar version that I am quite sure that does work. Unfortunately I'm not so sure how well it works because the math in calculating its effectiveness is more complex. I'll post a link in a couple days.

 

[ivymike]

well if you can't get your desired thrust out of it, you can at least turn it over and let it walk, eh?

 

[gearguru]

Here is one more note about the "negative radius".
In the most generic form of the formula for the centrifugal force "cf" the radius is expressed as a vector. It makes sense, because also the force is always represented as a vector; cf has not just size but also the direction. The remaining variables in the equation (mass "m" and angular velocity "omega&quot are scalars, they have size only.
When the object rotates, the direction of the radius vector pointing to the center of gravity of the mass is changing. The cf vector is "heading" in the same direction as radius vector. In the generic formula the radius vector defines also the direction of the cf vector.
To calculate only the size of the force, the equation was simplified: the radius now is actually represented by the length of the radius vector. The length of a vector is defined as the "absolute value" of the radius vector. The absolute value is always positive.
So - if we use the radius as a vector "r1", we can also use a vector "r2" negative to it (r2 = -r1); r2 has the same size (length), but opposite direction than r1. r2 only changes the cf direction (reverses it in this case), not size. Again: r1 and r2 and cf here are vectors!!!
Boy, wasn't it a simple question on the very top of this thread?
gearguru

 

[jamesxi]

I think that the equation is wrong:
Cf: centrifugal force in newtons
m: mass in kg
r: radius in meters

Cf = (2*Pi*RPM/60)^2 * m * r
(2*Pi*1000/60)^2 * 1 * .1 = 1096.6N
This is equal to 247 pounds of force

After figuring this out all over again, I came to the conclusion that r is in the wrong place so this is the right formula:
Cf = m * (pi * (RPM/60) * r)^2

Here is how I got the formula
f - force in newtons
a - acceleration in m/s^2
v - speed in m/s
pi - 3.14159
RPM - rotations per minute
r - radius in meters

f = m * a
a = v^2
v = (Pi * (RPM/60) * r)

f = m * (pi * (RPM/60) * r)^2
f = 1 * (pi * (1000/60) * .1)^2
f = 27.4 newtons
f = 6.16 pounds

 

[GregLocock]

no, Cf = m * (pi * (RPM/60) * r)^2 is WRONG because a = v^2 is WRONG.

Cheers

Greg Locock

 

[jamesxi]

Well with wrong in caps lock I must be wrong! I can't believe that I messed that up. Should read: a = (v^2)/r But using that equation I'm pretty sure its wrong too. The problem is that using the formula you gave me the numbers seem a bit high, but maybe the power of centripetal force is stronger than I think.

I would think that a 1kg weight spinning 1,000RPM on a 10cm radius(about 17 times a second) would generate no more than 50 pounds of force, so do you think that the actual number could be 250?

 

[quark]

The equation for centrifugal force is

F = m x r x (2 x Pi x N/60)[sup]2[/sup]

F= force in Newtons
m = mass in Kg
r = radius in meters
N = revolutions per minute

If you calculate the force it comes out to be approximately 111.8 Newtons.

One error in your post is you considered 1Kg to be mass of the object in the calculation, where as you say it is weight.

To convert weight to mass devide it by 9.81 because W= m x g

Regards,

 

[quark]

oops!

It is said as weight elsewhere. What is it exactly?

Also v = r x w(omega)

Where w = 2 x Pi x N/60 because there are 2 x Pi radians for one revolution. and a = rw[sup]2[/sup]

 

[Heyner]

Hi everybody!!!!

Did you see? we are still learning... every second. I was smiling all the time while reading this thread!!! "37 replies for a simple question" we say, but look where we are!

Let me try to help or make it worse:

1. Don't worry about weigth & mass of 1 kg (both valid). All you need is to have clear where and how to use the number.

2. F = m * a OK? so all we need is to find a, cause we have m = 1 kg.

3. Our a is the centrifugal aceleration, it permits the body to continue in a circular path, since it's trying to fly away all the time. Its direction: center of circle. Right?

4. so a = (w^2)*r where w is the omega Greglocock said. Of course we need it in radians per second, so the right conversion is: remember 1 revolution is 2*pi radians, ok? in some equation the "2" was missing, we all know the minute has (yet) 60 secs. No problem with that, conversion is like Quark said.

5. Ready. Multiply m by a. You got it. Astroclone let us know sometimes we pass over the error one time and another. Be careful. 10cm=0.1m oh, sounds so easy!!!!

Correct answer is 1096.6 Newtons. Remember this force has the same direction as aceleration vector, it is: center. Everything is consistent.

I'm not here to show you the answer, you already got it when I arrived. I just wanted to recognize your work: good thread, GOOD.

 

[chicopee]

Get it right-- unit of force in metric is expressed in Newtons not Kg. If I were your physics teacher which I suspect is part of an assignment or homework that you are doing, I would flunk you.

 

[IRstuff]

While on that subject, force direction inwards is tne centripetal force. TTFN

 

[Heyner]

IRstuff

You're right, I got a problem with centrifugal/centripetal.

Sorry.

 

[canox23]

Hello jamesxi
Here go to this site you can get a table on how to calculate a centrifugal foce this is a centrifugal force lab Website..

http://www.centrifuge.jp/calculation/

 

[IRstuff]

Heyner,

It's OK, centripetal force can be very non-intuitive TTFN