1. Angular Frequency

2. What in the World is it?! Angular Frequency is the scalar measure ofrotation rate. Huh?! Angular Frequency is how we describe themotion of a round object rolling around its center. Angular Frequency is how fast we say a CD isrolling. A synonym for angular frequency is angularvelocity, or speed. 3. What is it Measured in? The symbol for angular frequency is Angular Frequency is measured in Radians perSecond. That is to say, = 2/t being angular frequency, r being radians, and tbeing seconds 4. What are Radians? A radian is a measurement. In a circle, we have theradius. A radian is the distance of the radius on thecircumference of the circle. There are 2 radians on the circumference of everycircle. Or, in other words, there are 6.28... Radians on thecircumference of every circle. 5. How do we calculate angularfrequency? The way we calculate angular frequency is bysimply knowing Pi, and the amount of rotationsthe disk has undergone.So, before we begin, one rotation equal 2.Therefore, 2(rotation) equals radians.So, we have this disk. It rolls for 3 seconds, and rotates 5.7 times. What is its angular speed? 6. Continued... So, the time is 3 seconds, and it rotated 5.7times. We know the equation, 2(rotation)/t= So, plugging in the numbers:(2 * 5.7 * 3.1415)/3 = 11.94 radians per second We can address any other problem in a similarfashion. We simply plug in the number of rotations and amount of time. 7. Continued...What if we know the radians and time, but not theamount of rotations? Well, we can simply reverse the equation a bit: Original: 2(rotation)/t= Okay, the manipulation, Ill have to show my workin case you dont understand it well. Ill show thepicture on the next page. 8. Continued...Thus, to find the rotations is given by the equation Rotations = t/2 9. Converting radians to distance Now that we can find the radians of something,lets find out how far a disk went, using the sameproblem from before. The disk is moving at a rate of 11.94 r/s. If thatdisk has a radius of 2 meters, how far will it travel in three seconds? 10. Continued... Well, we know that a radian is the length of the radius. That being said, an equation to finddistance in meters given the time and radiansgoes as follows: m = radius* So, plug the numbers in! 2*11.94 = 23.88m The disk travels 23.88 meters. 11. How is this applied in the real world?Im sure that question is going through your mind.It sure went through mine. Well, think of the disk as a wheel on a car. Wecan find the speed of a car in meters by knowingsimply the radius of the wheel, and the amount of rotations it goes through. It can be used to find how many times a wheel turned in a certain distance. 12. Sources: http://en.wikipedia.org/wiki/Angular_speed http://en.wikipedia.org/wiki/Radians http://www.ck12.org/concept/Angular-Speed/?ref=%2Fconcept%2FAngular-Speed%2F