 As you might remember in the linear motion we had these very handy equations for constant acceleration that helped us to solve many of the problems quite quickly. Now the main question is do we have the same in the rotational case and the answer as you might can guess by the fact that I'm doing a video about it is yes there is. Well let's first go back and see what were those equations in the linear case. In the linear case I had that velocity as a function of time is my initial velocity plus acceleration times time. I also had that my position as a function of time is my initial position plus my initial velocity times time plus one half acceleration times squared. I had another equation for the position as a function of time which was it's equal to the initial position plus my average velocity which is my v initial plus v final over 2 times the time. And then I had a combination of my first and second equation which turned out to give us that v final squared is v initial squared plus 2A s final minus s initial. This last equation turned out to be very useful for any problem where we're not really caring about the time. Now let's look at the rotational case. The good news is not only do these equations exist for the rotational case they're actually very very similar so you don't have to remember anything new. All that you have to remember at the end of the TNDA is that whenever you see a v in the linear case you're going to replace this by the omega in the rotational case. Whenever you see s in the linear case you replace it by the theta and whenever you see a in the linear case you replace it by an alpha. The only thing that remains the same is the time which remains the time. So all we do is we replace the Latin characters by their Greek counterparts to express rotational motion. As a little side note if you really don't like these Greek characters well keep those equations and just treat them as rotational velocity as a function of time is initial rotation velocity times rotation acceleration time time. The whole thing will work. Now let me rewrite those equations. First of all we have a v so we replace it by omega so omega as a function of time is equal to my omega initial plus a becomes an alpha that rotation acceleration times time. That's it first equation done. Next one position we're going to replace the linear position s by the angular position theta. So theta as a function of time is theta initial plus v was omega, omega initial times time plus one half alpha times square. The next one my position as a function of time is again my initial position plus omega initial plus omega final over 2 which is my average rotational velocity times the time and the last one omega final squared is omega initial squared plus 2a is what again a is alpha alpha times s final minus s initial being my position so this time expressed as an angle theta final minus theta initial. And that's it we have our equations for rotational motion if acceleration is constant. So this is a very important thing. These equations only hold for the linear case if a is constant and for the rotational case the same thing applies the only work if the angular acceleration is constant.