• Distinguish between linear, angular, and general motion
• Define:
  • Distance and displacement
  • Average speed and average velocity
  • Instantaneous speed and velocity
  • Acceleration
• Name units of measurement for above definitions
• Use equations of constant acceleration to predict projectile motion

Kinematics is the branch of dynamics concerned with the description of motion.

Linear or Angular Motion requires two items: space and time.

Definition of Linear motion (rectilinear and curvilinear).

To distinguish between rectilinear and curvilinear motion, ask, "Are the lines straight or curved?"
 

Definition of Angular Motion.

Animation of linear and angular motion
 

General motion: a change in position typically results from a combination of linear and angular motion (e.g.., is human locomotion).

To analyze general motion, we often utilize the two following equations:

F = m · a, for linear conditions

T = I · α, for angular conditions

Kinematic Descriptor 1: Position (p): a location in space; meters should be used to describe position. For each dimension, one value is needed to describe position.

A sign, in addition to a magnitude will help describe the position of an object. For example, Is a runner 40 m from the start or 60 m from the finish? How might you avoid this confusion? You must describe P in reference to a fixed position.


 

Kinematic Descriptor 2: distance, and displacement (d): a change in position or, p₂ - p₁; meters should be used to describe distance and displacement; for two dimensional displacement, d = √(p_x2 - p_x1)² + (p_y2 - p_y1)²

What is the difference between distance and displacement? Distance is the length of the path traveled when changing position, and displacement is length and direction of the vector from the starting and ending position vector.

The difference between distance and displacement may be large or small, depending upon the circumstance.

400-m Race example...

Kinematic Descriptor 3: speed, and velocity (v): a change in position divided by a change in time or, v = (p₂ - p₁)/(t₂ -t₁)

Slope of a position-time graph equals velocity

Comparing position and velocity graphs
 

Speed, compared to velocity

Average Speed = Distance/Δ Time

Average Velocity = Displacement/Δ Time

Practice Problem: What was a marathon runner's average speed in finishing the 42.2 km race in 2 hours 10 minutes? Solution

Practice Problem: What is the average speed if you run a kilometer at 5 m/s and then walk a kilometer at 1 m/s ? Solution

Next, how do we quantify changing velocities?

Kinematic Descriptor 4: acceleration (a): a change in velocity divided by a change in time or, a = (v₂ - v₁)/(t₂ - t₁)

Average Acceleration = Δ Velocity/Δ Time

Shot Put Example:

Position-Time Data

Velocity-Time Data

Slope of velocity-time graph equals acceleration

Remember, that the direction of acceleration does not indicate the direction of travel, as I demonstrated by walking back and forth in front of class.

Instantaneous measures versus average measures:

 

Instantaneous cycling speeds

 

Average cycling speeds

 

Another example of an instantaneous measure

 

Instantaneous measures of velocity and acceleration are often more valuable than average measures (e.g., 100m sprint times).

 

 

Summary

   Displacement             Velocity                   Acceleration

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Projectile Motion

Notes from the ppt presentation regarding projectile motion. These will give you most of the information you will need concerning projectile motion.

An interesting demonstration on what happens to projectiles, as initial conditions are altered.

Practice Question:
Initial Velocity of Projectile

Vh = 5 m/s Vv = 10 m/s

Flight Time = ? Maximum Height = ? Horizontal Displacement = ?

Practice Question:
Initial Velocity of Projectile

V = 20 m/s at 45 degrees

Flight Time = ? Maximum Height = ? Horizontal Displacement = ?

Chapter Two Summary

1. Motion can be classified as linear, angular, or, most commonly, as a combination of both (general). Separating linear motion from angular motion makes it easier to analyze.

2. Linear displacement (vector quantity) is the straight-line distance from starting point to finish; linear distance is the distance of the path traveled.

3. Linear velocity (vector quantity) is the rate of change in displacement, relative to time; linear speed is the rate of change in distance, relative to time.

4. Linear acceleration (vector quantity) is the rate of change, relative to time, of velocity.

5. Projectile motion, any motion in which gravity is the only acting external force, can be described by a simple set of equations. It is necessary to describe vertical and horizontal motion independently when analyzing the motion of a projectile.