 In this video, I want to show you how to solve a simple rotational kinematics problem. A wheel has a constant angular acceleration. It makes 40 revolutions, while the angular speed changes from 20 rpm to 50 rpm. Find the angular acceleration. Now, first, as with all physics problems, let's have a look at what we know. We know that angular acceleration is constant, so alpha is constant, and we're actually looking for it. We know that it makes 40 revolutions, so we know that change in angle is 40 revolutions, while the angular speed changes from 20 rpm, so we know omega initial is 20 rpm to 50 rpm. So we have omega final is 50 rpm. Now, the first thing that you want to do when solving these type of problems is convert all the units to SI standards. Sometimes it works when not working in SI, but if you don't want to take any risk, convert it to standards. A revolution is a full circle, so if we turn word to radians, which would be the standard SI unit for this type of problems, we know that one revolution is 2 pi. Right. 40 times 2 times pi is 251, and I'm going to save this, so storage button in my variable A. 251.33 rads. Same thing for RPMs, revolutions per minute, what we want is rads per second. So same trick as before, one revolution is 2 pi rads, and per minute, so we want to multiply by one minute to 60 seconds. So we have 20 times 2 times pi divided by 60 seconds. So the rad, the revolution times this revolution per minute is cancelled by minute, so I get 2.09 rads per second. If you have a calculator that can store intermediate values, that would be a good idea to use that. So I'm going to try to store this in some variable on my calculator. So storage E. The omega-finance is 50 RPMs, so we do the same thing, times 2 pi rad over one revolution, times one minute is 60 seconds, this gives me 50 times 2 times pi divided by 60, gives me 5.24 rads per second. So again, I'm going to store this in my calculator, so store C. Now how do we find alpha? Let me remind you a little trick. All these Greek characters here look extremely complicated, but at the end of the day, it's not that complicated at all. Just think of linear kinematics. So here comes the trick. Linear kinematics, what was the acceleration given in, once given as A? What does the change in angle correspond to, corresponds to the change in position? What does the initial speed represent? That's V initial. What does the final speed represent? That's V final. So the question is, if we know that the acceleration is constant and we have a certain change in position, we have initial and final speed, we want to find the acceleration. What kinematics equation could have given us that? There are five kinematics equations for constant acceleration. We just go through the list of them and pick the one that has what we're given, as well as the unknown. Now here we don't know anything about time, which kind of eliminates four out of the five constant acceleration equations. The only one that doesn't have time in there is V final square, is V initial square, plus 2 times A times delta S. Which is perfect, right? Because we have the final velocity, initial velocity, and we have displacement. We look for the acceleration. So the acceleration is equal to V final squared minus V initial squared, divided by 2 delta S. So this is what we would have gotten in the linear case. Now let's just translate this back to the rotational case. Let's go back. Rotational case, we would have had omega final squared is omega initial squared, plus 2 times alpha times delta theta. Therefore, alpha is omega final squared minus omega initial squared over 2 delta theta. Now all I have to do is type this in my calculator. So my final I had stored in C. So in my case, V the omega final squared minus omega initial squared divided by 2, divided by the change in position, gives me 0.0458 rads per second square. And that is how we solve a simple rotational kinematics problem.