An electric turntable 0.750 m in diameter is rotating about a fixed axis with an initial angular velocity of 0.250 rev/s and a constant angular acceleration of 0.900 rev/s^2. (a) Compute the angular velocity of the turntable after 0.200 s. (b) Through how many revolutions has the turntable spun in this time interval?

Video transcript

Welcome back everybody. We have a wind driven cyclone that is following a circular pattern here. We're told a couple different things about it, right? We are told that it has um an average diameter of 60 centimeters or 600. m were also told that it's going pretty steady and has a steady angular acceleration of 0.4 to five revolutions per second squared. We're also told that its initial angular velocity is 0.5 revolutions per second. And we are tasked with finding over a time period of 0.750 seconds what the final angular velocity will be and the angular displacement will be Now for this we are going to be using some Kinnah Matic formulas. So first let's go ahead and find this final angular velocity. I'm gonna use the quadratic equation that says that our final angular velocity is equal to our initial angular velocity plus our angular acceleration times time billions of values. Here we have 0.5 plus 0.4 to five times 50.75 which you plug into your calculator. Get a final angular philosophy of 0. revolutions per second. Great. Now let's go ahead and move on to our angular displacement. A formula for angular displacement states that it is equal to our initial angular velocity times time Plus 1/2 hour angular acceleration times, time squared. So let's go ahead and fill into that some values for that too. 0.5 times 0.75 plus one half times 10.4 to times 50.75 squared. Which when you plug this into your calculator, you get 0.495 revolutions. Now we have found the final angular velocity and the angular displacement, which corresponds to answer choice. A thank you all so much for watching. Hope this video helped. We will see you all in the next one.