FIGURE EX4.24 shows the angular-position-versus-time graph for a particle moving in a circle. What is the particle's angular velocity at (b) t = 4s

Video transcript

Welcome back, everybody. We are tasked with finding what is the angular velocity at a time of T equals three and T equals 10. As you see, we are given a graph of time versus angular position. And this is going to help us in this way, we have that are angular velocity for any given point is the change in our angular position divided by the change in time. Another way to think about this, since we're given a graph of time versus angular Pa's is just the slope of the line at that point. So let's go ahead and calculate our angular velocity at a time equals three. So following time up here, we are trying to find the slope at this point. If you look at this, we can agree that from this point to this point, this particular segment has the same slope. So let's just calculate the slope of this line. And I'm gonna use this point for reference up here. So slope is just going to be your change in Y over your change in X. We see that we go up to pi and that we go over five seconds when you calculate this, this comes out to 1.26 radiance per second. Great. So now let's go ahead and find our angular velocity at a time of 10 seconds following our line up here. This is at this point, meaning we are finding the slope of this segment right here. So let's see here between this point and this point, it is going to be 10 seconds minus five seconds. But you'll notice in the Y direction we don't increase or fall. So this is just going to be 0/5, which is just equal to zero radiance per second. So now we have found the angular velocity at a time of three seconds and at a time of 10 seconds and this corresponds to our final answer. Choice of B Thank you all so much for watching. Hope this video helped. We will see you all in the next one.