00:01
In this example, we're going to make an estimate for the linear speed of the sun as it rotates with the milky way galaxy.
00:10
So here i've drawn out an artist's rendition of the milky way galaxy, which is really just simplified as something experiencing uniform circular motion.
00:23
So a big circle with a bunch of stuff inside, also going in a circle.
00:28
So inside the milky way galaxy is the sun, this red dot.
00:32
Here and it sits a distance ds away from the center of the galaxy as it rotates and the milky way galaxy will rotate with a period of 200 million years so given these facts let's see if we can find the linear velocity so if we recall the linear velocity can be related to the angular velocity omega and omega is related to the period of rotation it is 2 pi over the period.
01:12
So knowing that, we're almost where we want to be, we just have to change this r here now into our d -s, because we're not rotating out at the edge of the milky way galaxy.
01:31
Maybe if we called this r, right? we're actually making a smaller circle around the inside with radius ds.
01:42
So this should be ds, 2 pi over t.
01:47
So all we have to do now is plugging in...