00:01
So we have an astronaut attached to like a centrifugal arm that is spinning or it's increasing its angular velocity over time.
00:10
And we're told that it takes 40 seconds.
00:14
So 40 seconds for the angular velocity to be one revolution in 1 .2 seconds.
00:22
And we want to know during that first 40 seconds, what's the tangential acceleration? if the length of this arm is, let's see, 4 .6 meters, or basically the astronaut is 4 .6 meters from the axis of rotation.
00:40
So first off, to do this, let's write this in radiance per second.
00:43
One revolution is 2 pi radiance.
00:46
So 2 pi divided by 1 .2 seconds is going to give us our angular velocity.
00:54
And we could probably simplify this.
00:56
We multiply the top and the bottom by five.
01:00
We'll get like 10 pi over six radiance per second, which is 5 pi over three.
01:06
So the angular velocity is 5 pi over three radiance per second.
01:11
And we want to know what the linear acceleration and tangential acceleration is.
01:16
Well, the tangential acceleration is the angular acceleration times the radius of the circle.
01:23
And the angular acceleration is going to be the change in angular.
01:26
Velocity over time...