• Distinguish between linear, angular, and general motion
• Define and understand:
  • Position
  • Displacement and distance
  • Velocity and speed
  • Acceleration
• Understand the difference between instantaneous and average kinematic measures
• Understand how equations of constant acceleration can be used to understand projectile motion

Kinematics, Linear, and Angular Motion

Kinematics is the study and description of motion, without regard to the force that causes motion.

Linear and Angular Motion require space and time.

Definition of Linear motion.
 

Definition of Angular Motion.

Animation of linear and angular motion
 

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

One equation governs linear motion, while another equation governs angular motion:

F = m · a, for linear conditions, while

M = I · α, for angular conditions

Four Key Kinematic Descriptors:

Position (p): a location in space; meters should be used to describe position.

In addition to magnitude, the sign of the position vector is helpful in describing 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.

How many values are needed to describe the position of an object?


 

Displacement (d): a change in position (p₂ - p₁₎; meters should be used to describe 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 a scalar quantity (only magnitude) that describes the length of the path traveled. Displacement is a vector quantity (magnitude and direction) that describes the straight-line path between the start and end points. The difference between distance and displacement may be large or small, depending upon the circumstance (e.g., a 400-m race).

Velocity (v): a change in position divided by a change in time or, v = (p₂ - p₁)/(t₂ -t₁); another way to view velocity is: v = displacement/Δtime

A graphical perspective of the relationship between position, displacement, and velocity

What is the difference between velocity and speed? Velocity is

Velocity is a vector quantity that = Displacement/Δ Time

Speed is a scalar quantity that = Distance/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
 

Acceleration (a): a change in velocity divided by a change in time or, a = (v₂ - v₁)/(t₂ - t₁)

Shot Put Example:

Position-Time Data
Velocity-Time Data
 

A final, key point related to acceleration: the direction of acceleration does not indicate the direction of travel.

Instantaneous and Average Kinematic Values:

Average cycling speeds

Instantaneous cycling speeds

Sprinting Data

Summary:

   Displacement             Velocity                   Acceleration

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

Practice Question:
Initial Velocity of Projectile

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.