2. What in the World is it?!
● “Angular Frequency is the scalar measure of
rotation rate.”
● Huh?!
● Angular Frequency is how we describe the
motion of a round object rolling around it's center.
● Angular Frequency is how fast we say a CD is
rolling.
● A synonym for angular frequency is angular
velocity, or speed.
3. What is it Measured in?
● The symbol for angular frequency is ω
● Angular Frequency is measured in Radians per
Second.
● That is to say, ω = 2π/t
● ω being angular frequency, r being radians, and t
being seconds
4. What are Radians?
● A radian is a measurement. In a circle, we have the
radius. A radian is the distance of the radius on the
circumference of the circle.
● There are 2π radians on the circumference of every
circle. Or, in other words, there are 6.28... Radians on the
circumference of every circle.
5. How do we calculate angular
frequency?
The way we calculate angular frequency is by
simply knowing Pi, and the amount of rotations
the disk has undergone.
So, before we begin, one rotation equal 2π.
Therefore, 2(rotation)π equals radians.
So, we have this disk. It rolls for 3 seconds, and
rotates 5.7 times. What is it's angular speed?
6. Continued...
● So, the time is 3 seconds, and it rotated 5.7
times.
● We know the equation, 2(rotation)π/t=ω
● So, plugging in the numbers:
(2 * 5.7 * 3.1415)/3 = 11.94 radians per second
● We can address any other problem in a similar
fashion. We simply plug in the number of rotations
and amount of time.
7. Continued...
●What if we know the radians and time, but not the
amount of rotations?
● Well, we can simply reverse the equation a bit:
● Original: 2(rotation)π/t=ω
● Okay, the manipulation, I'll have to show my work
in case you don't understand it well. I'll show the
picture on the next page.
10. Converting radians to distance
● Now that we can find the radians of something,
let's find out how far a disk went, using the same
problem from before.
● The disk is moving at a rate of 11.94 r/s. If that
disk has a radius of 2 meters, how far will it travel
in three seconds?
11. Continued...
● Well, we know that a radian is the length of the
radius. That being said, an equation to find
distance in meters given the time and radians
goes as follows: m = radius*ω
● So, plug the numbers in!
2*11.94 = 23.88m
● The disk travels 23.88 meters.
12. How is this applied in the real world?
I'm sure that question is going through your mind.
●
It sure went through mine.
● Well, think of the disk as a wheel on a car. We
can find the speed of a car in meters by knowing
simply 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.
