00:02
Okay, so first let's see if we can get us some formulas.
00:09
So in the section before this one or two sections before this one, you learned a formula that was, if you knew the angle and the radius, then you knew this distance here.
00:27
It was s.
00:28
So that formula is s equals r theta, and to use that one theta has to be in radiance.
00:39
Okay, then you also know velocity or linear velocity from college algebra or sometime.
00:48
We'll just call it v.
00:50
And it's distance divided by time.
00:57
Okay, so if you're finding linear velocity in a circle, the distance is just going to be s.
01:03
Okay, so that's s over t.
01:08
But you know that s is the same thing as r theta.
01:12
So this is r theta over t.
01:16
But i can factor that r out and it's r theta over t.
01:22
So it's r times this thing, which is an angle over time.
01:31
That's angular velocity.
01:34
In my book, they call it omega.
01:36
So that's the formula we need linear velocity equals radius times angular velocity okay now you got some other problems here you got a lot of different units going on so we're going to have to straighten all that up we've got the diameter of the tires is 24 inches but then we've got the velocity in miles per hour so let's change both of those things to feet.
02:15
Okay, so diameter equals 24 inches.
02:20
That means the radius equals 12 inches, which is one foot.
02:27
Okay, the linear velocity is 15 miles in one hour.
02:36
So we gotta multiply by something that will get rid of the miles.
02:39
So we put the miles on the bottom, so they will cancel out.
02:42
And we wanna change it to feet, so we put feet on the top.
02:47
Which is bigger feet or miles miles is so put a one there and now you got to know how many feet there are in a mile okay well i know it's 52 80 okay also they want us to have minutes and not hours so we might as well change that too so we need to multiply by something that will make the hours go away so we got to put hours on the top and what we want to change it to on the bottom so i never think of it as multiplying or dividing, i just think of it as wherever it is, i have to put it in the other place to get rid of it.
03:25
If hours is on the bottom, i have to put hours on the top to get rid of them.
03:29
If miles is on the top, i have to put miles on the bottom.
03:33
Okay, which is bigger, an hour or a minute.
03:35
Well, an hour is.
03:36
So put the one there, and how many minutes in an hour? 60.
03:41
Okay, so look what happens.
03:43
The miles cancel, the hours cancel, and will be left with feet per minute.
03:48
Which is good because we have the radius in feet.
03:53
Okay, so we need 15 times 5, 280 times one divided by 1 times 1 times 60.
04:03
So let me get my calculator so i don't mess that up.
04:09
15 times 5282.
04:12
Divided by 60, 1 ,320, 1 ,320 feet in one minute or feet per minute.
04:30
All right, so here we go.
04:35
V equals r omega, so 1, 320 equals 1 times omega, so omega equals 1 times omega, so omega equals 1, 320 equals 1 ,000.
04:47
That's so weird.
04:48
Let's look at the units.
04:50
So we have v was in feet per minute, and then r was in feet, and then we have omega here...