0:00
All right, hello.
00:01
In this question, we're told we have a wheel, which is rolling across the floor and has some painted point p on it.
00:07
And at time zero, that point p is right next to the floor.
00:11
And then at some time t2, that point p is at the top of the wheel.
00:16
And in that time between time zero and time two, we're told that the wheel has rolled through one and a half revolutions.
00:24
So we have some change in our angle theta of 1 .5 revolutions.
00:29
And we're asked, what are the magnitude and angle relative to the floor of the displacement of p? so we start here at some point, and then this wheel is going to roll along and it's going to roll one and a half revolutions and then point p is gonna be there.
00:43
So this is gonna be our displacement vector of that point p.
00:47
We need to figure out what that is.
00:48
Well, in order to do that, we're gonna use the fact that it is now at the top of the wheel.
00:53
So we know that this is a height of two r and then it's horizontal displacement is gonna be some distance d.
01:00
How do we figure out that horizontal displacement? well, we know that our tangential distance, our linear distance is equal to our change in angle or our radial distance times our radius.
01:14
And so d is gonna be delta theta times r.
01:17
We have both of those values.
01:18
So this is just delta theta times r.
01:21
And so if we wanna figure out what our displacement vector d, big d appears with the vector hat, we would say that it's a vector...