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?
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
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
Mini-Project #1