00:01
Let's say we have a ring with a radius r and a mass capital m, and there is a particle with a mass little m a distance x away from it.
00:10
We want to find the force acting on the ring.
00:12
So first off, let's find the gravitational acceleration.
00:15
We can write this, we assume that the ring has a linear mass density, which is m over 2 pi r.
00:23
And what we'll do is draw a line connecting a certain mass element to this point.
00:30
And obviously the only point of this force that matters is going to be the horizontal component.
00:36
So this will be lambda times r d theta, where d theta is going around the circle.
00:45
And in fact, since all these points, there's actually an easier way to see this.
00:49
Since every point along the circle is the same distance away, what we'll have is the acceleration is going to be g times m over, and then the distance is going to be x squared plus r squared.
01:05
And so the force that it experienced, sorry, the direction here is going to be in the negative x direction...