A wheel is rotating about an axis that is in the z-direction. The angular velocity ω_z is -6.00 rad/s at t = 0, increases linearly with time, and is +4.00 rad/s at t = 7.00 s. We have taken counterclockwise rotation to be positive. (c) What is the angular displacement of the wheel at t = 7.00 s?

Video transcript

Welcome back everybody. We are looking at a rotary dining table and we are told that at time equals zero, that its initial angular velocity is equal to negative five radiance per second Just a couple of seconds later. So we'll have an initial final uh just a couple seconds later at 5.5 seconds we have that our angular velocity is now eight 0.5 radiance per second. And we are tasked with finding what our total angular displacement is. I'm gonna use a kid, a magic formula here. That says that our angular displacement is equal to one half times our initial angular velocity plus our final in velocity over our entire time interval. What we went from 0 to 5.5 seconds. So our entire time interval is just 5.5 seconds. Let's go ahead and plug in some values here. We have that our angular displacement is equal to one half times negative. Five plus 8. Times 5.5. Which when you plug into your calculator you get 9. radiance corresponding to our final answer choice of D Thank you guys so much for watching. Hope this video helped. We will see you all in the next one.