1. Distance and Displacement Distance: How far an object travels to get from one point to another. This has just a magnitude.  It is a scalar. Displacement: The overall (RESULTING) change in position only. Displacement = Position Finish – Position Start This has BOTH magnitude and direction It is a Vector.

2. VECTORS Have both a magnitude and a direction Used to represent velocities, acceleration, forces, anything that has both a magnitude and a direction. Vectors can be added, but their directions must be considered. The sum of two or more vectors is called a RESULTANT. A resultant is the combination of 2 or more vectors. When numbers are added you get a result, when vectors are added you get a resultant

3. First Example Distance and Displacement Tommy walks around a square table 2 meters in length on one side. How far did Tommy walk? (How far asks for a distance) Start/Finish Walked 2 m The distance Tommy walked is 2m+2m+2m+2m or simply 8 meters Tommy’s Displacement is 0 meters. That is because Tommy finished where he started. In the end there was one change in his position. What is Tommy’s Displacement?

4. Second Example of Distance and Displacement A girl standing still throws a ball upwards 6 meters in the air, and catches it on it’s return at the same height it was thrown. How far did the ball travel? (Looking for a distance again) 6 meters up 6 meters down The ball travels a total distance of 12 meters. The displacement here again is zero meters. The ball lands at the same spot it was thrown. In the end the ball’s position did not change. What is the ball’s Displacement?

5. Last example of Distance and Displacement Jean runs 10 meters to the East, stops and then runs 4 meters to the west. What is Jeans displacement? Runs 10 meter East Runs 4 meters West Start Finish Displacement (A.K.A.) Resultant The displacement is 6 meters to the East The distance traveled is simple 14 meters.

6. Rotational vs. Circular motion When a planet orbits a star, or when a car makes a turn we have objects that can be thought of a single point that is moving around another point that is outside the object. Radius of motion Velocity of object Path of motion Center of motion (outside the moving object) When a planet rotates on it axis, or when a wheel spins around its own center, we can view each of the nearly infinite number of points in these objects going through circular motion (not a fun idea) or instead we can view them as a single object going through rotational motion (an object spinning around a point inside the object itself) Center of motion (inside the moving object) Rotation of object

7. The need for a different prospective on displacement If we have a disk that rotates one time, what is the displacement of a point on the disk, and what is the displacement of the disk itself? Based on our Cartesian system the displacements of both are that there is no displacement So if we want to describe the rotation of the disk (or any point on the disk) we need a system that measures angles.

8. Another position System If we look at the disk as a whole and the angle that the disk rotates through we will have a non-zero value, even though the individual points on the disk return to there starting point.  = 90 O  = 180 O  = 270 O  = 360 O So for rotational motion we describe a disk’s position using an angular system. We will call the disk’s orientation (the position of a point on the disk) its angular position (  ). Important Note: There is no limit to how big  can be. For trigonometry the sine, cosine, and tangent function values repeat in cycles from 0 O to 360 O. So is some cases 0 O can be considered equivalent to 360 O, but that does not make them equal.

9. Angular displacement (  ) So even though we are using a new system to measure (or describe) an object’s position none of our definitions and relationships such as displacement, velocity, speed, acceleration, momentum, work, or energy change To make a distinction from the displacement we have always worked with in our “traditional” Cartesian system (  Pos) and this angular displacement we always use The complete term “Angular Displacement”. Angular Displacement = change in Angular Position By definition displacement is the change in position, and definitions always apply (otherwise they would not be a definition)

10. Angular displacement part 2 Reference line to measure positions from. Angular Position:  = 30 O clockwise Reference line to measure positions from. Angular Position:  = 30 O Counterclockwise The definition of displacement does not change So we need to give the magnitude of the angle, but also state a direction such as clockwise or counter clockwise

11. Units for Angular displacement Any of the following can be used to describe angular displacement 1)Revolutions (1 complete circle) 2)Degrees (360 degrees = 1 Revolution) 3)Radians (2  Radians = 360 degrees = 1 Revolution) 4)Gradians (a British unit for angles there are 400 gradians in 1 circle (or revolution)