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# The angular velocity of a fan blade is 6.2 radians per second.

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The angular velocity of a fan blade is 6.2 radians per second.

Approximately how many revolutions does the fan blade make in 1.6 minutes?

I think it would be 15.3  revolutions ?

Apr 1, 2020

#1
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Ok I will show you how I tackle these.  Once you get the hang of it, my way is really easy.

First make a list of all the rates you know that are relevant.

$$\frac{6.2 radians}{1 sec},\qquad\frac{60sec}{1min},\qquad \frac{2\pi radians}{1 revolution},\qquad \frac{1.6minutes}{1}\\ ~\\find\qquad \frac{?revolutions}{1}\\$$

Since the first 3 of these fractions have units top and bottom they can be turned upside down.

So, for example, it is correct to say   1sec/6.2 radians

You can only turn a fraction upside down if there are units both top and bottom!

Now I want to end up with revolutions on the top and I want all the other units to cancel out.

So I start with revolutions on the top and then I keep multiplying by the correct thing to cancel out the units on the bottom.

like this:

$$\frac{1 revolution}{2\pi radians}\times \frac{6.2 radians}{1 sec}\times \frac{60sec}{1min}\times \frac{1.6minutes}{1}\\ \\~\\ =\frac{1 revolution\times 6.2\times 60 \times 1.6}{2\pi\times 1\times 1\times 1}\\~\\ =\frac{6.2\times 60 \times 1.6}{2\pi}\;\;revolutions\\~\\ =94.7\;\;revolutions.$$

Coding:

\\~\\
=\frac{1 revolution\times 6.2\times 60 \times 1.6}{2\pi\times 1\times 1\times 1}\\~\\
=\frac{6.2\times 60 \times 1.6}{2\pi}\;\;revolutions\\~\\
=94.7\;\;revolutions.

Apr 1, 2020
#2
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Hey Melody !

Hope your liquor is supply is holding out .....

That is the way  I do these (and other) questions too.....I 've been putting all of the dimensions down and striking through them to show how they cancel and you're left with what you are questioning...but I wonder if anyone out there 'gets it' sometimes !       Is dimensional analysis no longer taught?   HOW will anyone EVER become an ENGINEER ?!  ....and get calculations correct        Haha     ......

ElectricPavlov  Apr 1, 2020
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I was never taught this.

I had to teach a unit of nursing maths at college.

Nurses use the most bizarre 'formulas' that make no sense.

Nurses just memorize these 'formulas'. it is not proper maths by any stretch.

I could not get my head around them. I cannot remember things that don't make sense.

However, the units are horrendous. I had to 'invent' some method to deal with all the rates.

This is what I came up with.  It worked a treat.  I thought I was very clever 'inventing' this.

Of course, the students went on to other teachers that demanded they use these ridiculous archaic nursing 'formulas'

So although I gave them an easy to use method that actually made sense, it probably didn't help them a lot in the long run.  What a pity.

Melody  Apr 1, 2020
edited by Melody  Apr 1, 2020
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Yes...I've seen nuurses make mistakes when a curve is tosses at them and a drug all of a sudden comes with a different concentration/strength.  They have infusion pumps now in which you enter all of the parameters and it will calculate the infusion rate for you.....I think they just do that and assume they got it all correct wiithout knowing the method the infusion rate is calculated...kinda scary, but they woud often ask me if everything looked 'OK"......

Perhaps you heard of the 'rule of sixes'   'point sixes'   etc when mixing or compounding infusions so that the ml/hr displayed on the pump was

mg/kg /min etc ?

ElectricPavlov  Apr 1, 2020
#5
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wouldnt you do 1.6* 60 seconds = 84 radians

then 84/2pi ? = 15.3 ?

jjennylove  Apr 1, 2020
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No I haven't heard of that.

Yes, nurses just type in the parameters and so long as they enter it properly the machines do the calculations.

There is really no problem with this, it is no different than an engineer using an advanced calculator.

Nurses do have the 'formulas' drummed into them and intelligent nurses do work them out and remember how to use them.

It is a bit like learning the logic of language rather than the logic of maths. The rules must be learned and followed but the logic behind the rules is a bit hazy.

I used to tell my kids that they needed to be able to work problems out themselves as they may find themselves in a war or third-world situation where facilities were much more basic.

Melody  Apr 1, 2020
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Hi Jenny,

You have not used the 6.2 radians per second bit.