Linear Kinematics

Objectives

  • Examine how to describe a body's position
  • Define how to determine the number of independent quantities (called degrees of freedom) necessary to describe a point or a body in space
  • Define how to measure and calculate changes in linear position (displacement ) and the time derivatives velocity and acceleration.
  • Describe how to present the results of a kinematic analysis
  • Explain how to directly measure position, velocity , and acceleration by using motion capture systems or transducers

Description of Position

Is a runner 60 m from the start or 40 m from the finish?

Line up on the 20 yd line.

What is the position of my knee?

Right Handed GCS LCS

x, y, z, θx, θy, and θz

  • How many camera views are needed to obtain x, y data?
  • How many camera views are needed to obtain x, y, z data?
  • How many points are needed to obtain θx, θy, and θz?

Two-Dimensional Calibration

  • Scaling Rod
    • s = actual length (m) / digitized length (pixels)
    • x = su
    • y = sv
  • Practice with Dartfish


Distance: The length of a curve or line

Displacement: Change of position (Straight-line distance from start to finish)

Time Derivatives

  • Speed: Distance / Time
  • Velocity: Displacement / Time
  • Acceleration: Velocity / Time

Projectile Motion

A Projectile is any body that has been set on its path by some force and continues in motion by its own inertia. (Gravity has a major effect on motion).







Examples of Projectiles include: Arrow, Basketball, Shotput, Human Body,Tigers

Let's begin simply with purely vertical motion
Projectile Cartoon

Now let's add horizontal motion

Horizontal and vertical components are independent

Equations of motion for projectiles

Characteristics of projectiles

Demonstration on what happens as initial conditions are altered

Another projectile cartoon

  • 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 = ?
  • Things get more complex when takeoff and landing heights are different
    Flight Time Equation

    Shot Put Example

Mini-Project #1