INSTRUCTOR: Let's take a look at an example of angular and linear velocity. Two particles are spinning on a disk. One particle is 12 centimeters away from the center, while a second particle is 15 centimeters away. So looking at these concentric circles, we could think of one particle being here 12 centimeters away from the center. We can think of the second particle here 15 centimeters away from the center. 

It says, if it takes 6 seconds to make a rotation, determine the angular and linear velocity. Omega, or angular velocity, is equal to theta divided by t. Notice that this formula does not involve the radius, and therefore, the angular velocity is going to be the same for both of these particles. 

And because it takes 6 seconds to make one rotation, one rotation would be a theta of 2 pi radians. And the time it takes is 6 seconds. So this simplifies nicely to pi over 3 radians per second. 

Now, we know from algebra that the velocity of an object is equal to its distance divided by the time. But because these particles are spinning around a circle, the distance is actually arc length, or r times theta. So because the radius of these two particles is different, the linear velocities will be different. 

So for the particle that's centimeters away, the linear velocity will be equal to the radius, 12 centimeters, times theta, which is still 2 pi. And the time is still 6 seconds. 

Here the 12 and the 6 simplify. That would change to a 1. This would change to a 2. So the linear velocity for the first particle would be 4 pi. This would be centimeters per second. 

Now for the second particle, it's going to be the same, except now the radius will be 15 centimeters. So it's actually going to travel further in the same amount of time. 

In the numerator, we have 15 times 2. That's 30. 3 divided by 6 would be 5. So this would be 5 pi centimeters per second. Again, notice how the particle that's further out on the disk is going to travel further in the same amount of time. 

There is one more thing I should mention. Notice there are two formulas for linear velocity. I like using r theta divided by t because it reminds me that r theta is a distance. But since theta divided by t is equal to omega, we could use the formula r times omega. And that would have been a little less work because we did find the angular velocity in this first step.