## DarkBlueChocobo one year ago Help with application problem

1. DarkBlueChocobo

A paddle boat is traveling down a lake at 15 mph. If the paddle wheel is 8 ft in diameter, how many revolutions per min is it rotating

2. DarkBlueChocobo

|dw:1443836986859:dw|

3. DarkBlueChocobo

so the radius of the wheel is 4 ft then

4. DarkBlueChocobo

but first wouldnt we have to change units

5. DarkBlueChocobo

|dw:1443837060765:dw|

6. DarkBlueChocobo

|dw:1443837124936:dw|

7. DarkBlueChocobo

Doesn't this give us the angular speed?

8. DarkBlueChocobo

@zepdrix

9. zepdrix

Umm umm umm, I'm getting a little confused by your break down of the units. Lemme show you how I'm thinking about it.$\large\rm boat~speed=\frac{15\color{orangered}{(miles)}}{1\color{royalblue}{hour}}=\frac{15\color{orangered}{(5280ft)}}{\color{royalblue}{60\min}}$So we get that the boat travels at a rate of:$\large\rm boat~speed=\frac{15(5280)}{60}\frac{ft}{\min}$And the circumference of our wheel is:$\large\rm C=\pi d\qquad\to\qquad C=8 \pi ft$The distance around the wheel, the circumference, is one full revolution. So our wheel is moving at this rate:$\large\rm wheel~speed=8\pi\frac{ft}{rev}$ So then ummmmm, we divide I guess? $\large\rm \frac{15(5280)}{60}\frac{ft}{\min}\div8\pi\frac{ft}{rev}$Sorry I'm a little rusty on these types of problems :) lol

10. zepdrix

$\large\rm =\frac{15(5280)}{60}\frac{\cancel{ft}}{\min}\times\frac{1}{8\pi}\frac{rev}{\cancel{ft}}$

11. zepdrix

Mmm I need a brief refresher on this stuff XD What is this type of problem called? I'll Google it. Something with rotational motion?

12. DarkBlueChocobo

Well the beginning of it was Angular speed and then you converted it to linear speed basically because they are related

13. zepdrix

I guess I made it a little bit of extra work by writing the angular relation like this. I should have written it like this: $$\large\rm \dfrac{1rev}{8\pi ft}$$ And then it's just a multiplication problem, canceling out the units in the long string as you did.$\large\rm \left(\frac{15miles}{hr}\right)\cdot\left(\frac{5280ft}{mile}\right)\cdot\left(\frac{hr}{60\min}\right)\cdot\left(\frac{1rev}{8\pi ft}\right)$

14. zepdrix

I think you just had your last term a little off, ya? :o The wheel spins 8pi every revolution.

15. DarkBlueChocobo

It seems so :<