# Math units

1. May 3, 2004

### hpdrifter

I have a simple math problem. I know the basic formula, but am too far removed from math lessons(50 years of age) to figure it out. I know you require like units to derive an answer.

A 200 gram object is rotated around a 4' radius at 100 mph. What is the centrifugal force?

I know(at least think) Fc=m*v²/r, but can't figure the units out to come to a clear enough answer.

If I use the 200 grams, would I need to convert the 100 mph to fps(147) or m/s(no clue at this time) and the r(4') to meters?

Or, to keep it simple(to me) could I just use say 8oz*147²/48" and yield ozs and divide by 16 to get pounds. I get 225 punds with this method and it seems like quite a lot of centrifugal force.

2. May 3, 2004

### arildno

OK:
What you need to choose first, is what units you want to express "force" in.
The most common is in "newtons", which satisfy:
newton=kg*m/s^(2).
Hence, to express the given quantities in newtons, you'll have to change mph's into m/s, and inches ('?) into meters (In addition, 200g=0.2kg)
I'm not good at the BE units, so I'll leave that alternative to others.

3. May 3, 2004

### hpdrifter

thanks for info.

I, being from the USA, prefer pounds,psi, or whatever the units would be expressed as. Slugs?

4. May 3, 2004

### arildno

I think slugs is the word for it, yes
(It has always struck me as something creepy..)

5. May 3, 2004

### HallsofIvy

Staff Emeritus
I, also, am from the United States, but for a problem like this I would certainly use the metric system. The mass is 2 grams= 0.002 kg. The radius is 4 feet= 1.22 meters (approximately) and the speed is 100 mph= 146.67 feet/sec= 44.8 m/s.

The unit of mass in the English system (which you never hear about because mass is only important in scientific calculations and scientists alway use the metric system), the mass corresponding to a one pound weight at the surface of the earth (weight divided by 32.2 f/s2), is sometimes called a "slug", sometimes a "poundal". They are the same thing.

6. May 3, 2004

### krab

On getting units right, I have a system that has helped me in 30 years of doing physics. I never worry about rules such as "multiply by 2.54 to convert inches to cm", because eventually I would always forget whether to multiply or divide. Remember formulas like 2.54cm=1in, because that contains all the info you need.

Remember that physical quantities have units. E.g. "length = 6" has no meaning. These units are used in physics formulas exactly as if they are algebraic variables. Now take conversion formulas like say 2.54cm = 1in, and convert them to the form 1=something. For example,
$$1={2.54\,\mbox{cm}\over 1\,\mbox{in}}={1\,\mbox{in}\over 2.54\,\mbox{cm}}$$
Since the formula really now is 1, with no units, you can multiply any physical quantity by it without changing it. Example: you have L=6cm and want inches. Try
$$L=6\,\mbox{cm}=6\,\mbox{cm}\times{2.54\,\mbox{cm}\over 1\,\mbox{in}}$$
and note that the cm do not cancel, so obviously this is not helpful. It is still correct, but you want inches, not cm^2/inch. So try
$$L=6\,\mbox{cm}=6\,\mbox{cm}\times{1\,\mbox{in}\over 2.54\,\mbox{cm}}={6\over 2.54}\,\mbox{inches}$$
because now the cm do cancel.

Use this system, plus the conversion formulas (not recipes), plus additional info like 1newton=1kg-m/s^2 (as arildno said), and you'll never go wrong.

7. May 3, 2004

### hpdrifter

thanks all.

HallsofIvy, that was 200 grams, but I got your meaning.

krab, thanks for the refresher. It's been a while. I use cross multiplication(term when I attended school or ratio) all the time.

Me thinks the formula is not correct, or better yet my math skills have deteriorated.

Through my calculations I get ~225 poundals(slugs)or 329 N. It seems awfully heavy for a golf club(driver head at 200 grams) that is swung at 100 mph.

I was just trying to compute what the ~w of a driver head is during the bottom of a good golf swing. Impact notwithstanding.

8. May 3, 2004

### krab

329 nt is correct. This is 74 pounds. (I don't know what you mean by 225 slugs: slug is a unit of mass, not force.) But in any case, it's a lot of force. I once explained this to my brother (an avid golfer), and he told me it helped him understand the forces he applies. It also explains why beginners who try to "kill" the ball invariably ground the club head.

9. May 3, 2004

Centripetal...

10. May 4, 2004

### hpdrifter

thanks again krab. I thought(key word) that slugs was a unit of momentum.??? Well, since I'm not trained in Physics, let me guess, momentum is a measure of mass? M*V?

cookiemonster, isn't centripetal the counter force of centrifugal????? So to speak anyway. I realize it's probably not the correct verbage for Physicists.

11. Jul 21, 2007

### Bryan Parry

:surprised Nej. The poundal (pdl) is the unit of force when m = pound and a = ft/s/s. It is around 1/32.17405lbf

The slug is a unit of mass when the unit of force is the pound-force instead of the poundal (and when the unit of length is the foot). This, then, is equal to around 32.17405lbm.

12. Jul 21, 2007

### cristo

Staff Emeritus
This is a very old thread to dig up! You are, however, correct: http://en.wikipedia.org/wiki/Poundal

13. Jul 21, 2007

### belliott4488

I hate this lbf/lbm stuff, but until all the engineers in the US agree to give them up, we're stuck with them (in the US, that is). :grumpy: I work at an applied physics lab and have to deal with this all the time, and it always forces me to stop and think it through all over again - a major waste of brain cells.

Here's the answer, unless I get it wrong again

The slug is the unit of mass that allows you to use lbf (pounds force), feet and seconds in a "rationalized" sense, i.e.

1 lbf = (1 slug) X (1 ft/sec^2)

(compare to 1N = 1kg x 1 m/s^2 )

On the other hand, one pound mass (lbm) is the mass that has a weight (force) of 1 lbf at the Earth's surface, i.e.

1 lbf = (1 lbm) X g, where g is the average gravitational acceleration at the Earth's surface, 32.xxx ft/sec^2.

Thus,

1 lbf = 1lbm x 32 ft/sec^2, which then must give
1 lbf = (1/32 slugs) x 32 ft/sec^2, from the eq. above, so

1 slug = 32.xxx lbf (I don't recall the exact number - I think someone provided it above)

I try to keep a picture in my head of a slug as a 32 lb rock or something, just to help avoid getting my conversions backwards.

Last edited: Jul 21, 2007
14. Jul 23, 2007

### Bryan Parry

I didn't realise at the time! I was just looking thru threads and had something to add!

15. Jul 23, 2007

### Bryan Parry

I don't see the problem. Slug has to do with slugging someone (as it were), or old slugs in cannons; nothing to do with slimy animals! :D

A way to get rid of this small, slimy creature notion might be to think of slugging someone; would you slug them if you hit them with a slug = animal, or would you slug them if you hit them with a 32lbm lump? :)

In an absolute system, if m = slug, then f = pound-force, and if m = pound-mass, then f = poundal [1/32.17405lbf]. It's quite simple, really. Some people, of course, will use pounds for both mass and force, just as some will use kilograms for both mass and force. This is probably to be avoided for the most part.