00:01
For this problem, we're given that a ferris wheel at a carnival has a diameter of 48 feet, and it turns at a rate of five revolutions per hour.
00:11
We're being asked to find the angular speed of the wheel, and also the linear speed of a passenger riding the ferris wheel.
00:20
So let's get started.
00:22
What i have up here on the screen is some notes that might help us.
00:26
It's to give the idea that one revolution can be described in different.
00:30
Ways.
00:32
One way is to describe in terms of the angle that it makes.
00:36
So one revolution around a circle is two pi radiance or 360 degrees.
00:43
Another way to describe it is the linear distance that someone traveling around a circle would go.
00:51
So if you think about how far the distances around a circle, you're actually thinking about the circumference.
00:58
And one way to calculate that is diameters.
01:01
Times pi.
01:03
So we have all of the information here.
01:06
And one way to answer these two questions is to actually do a little bit of unit conversion.
01:12
So i'll show you that way.
01:14
First we start off with what we're given.
01:16
We're given that this ferris wheel turns at five revolutions per hour.
01:22
So i'm going to write it as five revolutions over one hour.
01:26
Now since i want the angular speed, i need to change their revolutions into radiance.
01:34
And so this is how i do that.
01:36
I know that one revolution is equivalent to two pi radiance.
01:41
So i'm going to put one revolution down here, the bottom of my second fraction...