 Now we're going to come up with an expression for the velocity of objects undergoing uniform circular motion. So what speed is an object undergoing uniform circular motion actually travelling at? Well we know that for a constant velocity the speed v is equal to the distance travelled divided by the time taken to travel that distance. So let's investigate one revolution which is an object travelling once around the circle. We know that the distance the object has travelled is the circumference of the circle. If you remember the circumference of a circle is equal to 2 pi times the radius of the circle. So for an object undergoing one revolution of the circle the distance is equal to 2 pi r. Now the time taken to complete one revolution around the circle is the time of the period which we're going to call big t. So for example the period of the earth travelling around the sun which we discussed earlier is 365 days. And that's the period of the earth's orbit. So if we look back at our velocity equation and we plug in the values that we've derived we see that v, the velocity of an object undergoing uniform circular motion is equal to 2 pi r the radius of the circle divided by big t, the period. And there you have it. The speed of an object undergoing uniform circular motion is equal to 2 pi r on t. So now we know the magnitude of velocity. What is the direction of the velocity vector? We know that an object undergoing uniform circular motion is travelling along the circumference of a circle. To undergo this motion the velocity vector of the object must be tangential to the circle at every point. To see this let's consider the velocity of different points along the path of motion. On the top of the circle in our example the object is moving left so the velocity vector must point left. And if we look at the velocity at the bottom of the circle we know that the object must be pointing right so the object is moving rightwards. If we look at the left side of the circle the object is moving downwards so the velocity vector must point down. We can see that at every point on the circle the velocity is pointing tangentially to the circle. So in summary the velocity of the object undergoing uniform circular motion has a magnitude of 2 pi r on t and the direction of the velocity is tangential to the circle on which the object is undergoing uniform circular motion.