00:01
So in this problem, we're given that a point on a flywheel with a radius of 12 inches rotates at a rate per second.
00:05
We're not told what the rate is.
00:07
I don't know if it's general or if it's just missing.
00:09
We'll solve it in general and then we'll discuss what to do if we have it.
00:13
We want to know what the linear speed is in centimeters per minute.
00:17
So we start with this.
00:19
We start with the angular speed.
00:25
Omega is theta over t.
00:27
So whatever the angle traveled, theta, divided by t time, gives us our omega.
00:33
Angular speed and that's going to be right here at a rate per second if we knew what that was let's say it rotated two times per second then our theta would be four pi two times two pi two times around so right now we'll have to just call this rate per second our omega we have this equation for linear speed right here so my v is the linear speed s is the arc length and t is the time so whatever arc length it travels divided by how long it took to travel that gives me my v, my linear speed.
01:15
And then we have this equation right here, s equals r theta.
01:20
The s is the arc length.
01:22
So that would be the length of this green arc here.
01:26
And of course, that is derived from whatever the radius is times whatever the central angle that we traveled in radiance.
01:34
And so what we have to see here is that we have an s here and we have s defined...