 So now we're going to introduce circular motion and simple harmonic motion, abbreviated SHM. So in uniform circular motion, the motion was defined as motion in a circle at constant speed. The in a circle part means that my radius is constant as it moves around. And the constant speed is particularly in this case referring to the angular speed. But even though r and omega were constant, my other coordinates are not constant. So if I were to represent the position of that particle in x or in y, from trigonometry, x is going to be r cosine theta, y is going to be r sine theta. But these things aren't constant because theta isn't constant as it moves around the circle. As a matter of fact from our angular motion studies earlier this semester, we saw that theta is a function of time where I have my initial angular position plus the angular speed times time. Now I could rearrange these two terms and it turns out that this one is a little bit more common where I put the omega t first and the plus theta initial second. So let's look at these positions in x and y. And I've got my theta and now I've got my theta equation. I'm going to combine that in there and what that's going to give me is these two equations for my x and y, r cosine omega t plus theta initial and r sine omega t plus theta initial. Now graphically if I look at my little black dot in here moving in circular motion around the circle, then I can track my position in x with this little blue dot going back and forth. And I can track my y position with this little red dot which is going up and down. And if I actually track exactly how fast those two dots are moving, the blue one and the red one, I see that it plots out a cosine curve and a sine curve. Now in summary I've got my equation for the horizontal position as a function of the time variable and it also depends on the radius, the angular speed and the initial angular position, which I'm now going to call phase. If I were to look at the equation for the y position, y represents the vertical position, but everything else in this equation still represents the same quantities. So these are our equations for circular motion and we're going to see through the next few videos how this has the same form as general simple harmonic motion.