At some point, you may have whirled an object about your head at a constant speed. A string tied to the object and the other end of the string held in your hand defined the circular path of the object.
If you released the object at some point and watched it fly away, you may have noticed that it flew away in a line that was tangent to its circular path at the instant of release. What’s tangent? (line “just touches” the curve).
Ok, so we’re talking about circular motion… A circle is a plane figure uniform motion in a circular path is motion in a plane so we’ll use vectors to describe the motion.
First, let’s define uniform circular motion: the motion of an object with a constant or uniform speed. [slide 2].
Ex: Suppose you’re driving a car…you’re such a good driver that you can get the car to follow the path of a perfect circle with a constant radius. And suppose that as you drove, your speedometer maintained a constant reading of 10 mi/hr.
**Look back at the scenario… [underline perfect circle with a constant radius & speedometer maintained a constant reading of 10 mi/hr].
Speed and Velocity in a Circular Path
Now let’s take a look at how physics views circular motion.
For starters, an object moving in uniform circular motion would cover the same linear distance in each second of time. When moving in a circle, an object travels a distance around the perimeter of the circle.
So let’s say your car were to move in a circle with a constant speed of 5 m/s, then the car would travel 5 meters along the perimeter of the circle in each second of time. [slide 3]
I want you all to take a minute or so and reflect on that. Make sense?
Ok, so, let’s deviate and talk a little geometry. I have here a circle [draw diameter and radius – ask students to identify diameter and radius]. What do we call the perimeter of a circle?
The circumference. Yes. And how do we calculate the circumference of a circle? C = ? C = 2 * π * r where r represents the radius.
“This means if your car were to move in a circle with a constant speed of 5 m/s, then the car would travel 5 meters along the perimeter of the circle in each second of time.”
Still make sense? Ok, then suppose my car is moving around this circle and the circumference of this circle is 5 meters. My car is moving at a uniform speed of 5 m/s, how long does each cycle around this circle take? [1 second]
[slide 4] A couple more definitions: For the purpose of physics, we call the circumference of the circle a revolution. And the time required to make one complete revolution (cycle) is called the period. We use the variable T to represent the period of motion.
Average Speed [slide 5]
Ok, let’s say we want to determine the speed of…