• Part I: Define and distinguish between linear, angular, and general motion
• Part I (cont.): Define and understand the concepts of:
  • Position
  • Distance and displacement
  • Average speed and average velocity
  • Instantaneous speed and velocity
  • Acceleration
• Part II: Use equations of constant acceleration to better understand projectile motion

Kinematics, Linear, and Angular 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, one might simply ask, "Are the lines straight or curved?"
 

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. A good example of general motion is human walking.

To analyze general motion, we often utilize the following equations and four primary kinematic variables (position, displacement, velocity, and acceleration):

ΣF = m · a, for linear conditions

ΣT = I · α, for angular conditions

Position, Displacement, Velocity, and Acceleration

Let's use some experimental tennis data and the following central difference equation to help us better understand position, displacement, velocity, and acceleration.

Position (p): a location in space, that should be described in meters. For each dimension, one value is needed. As with other vectors, a sign and a fixed reference position are necessary to describe position.

Displacement (d): a change in position or, p₂ - p₁; for three-dimensional displacement,                d = √(p_x2 - p_x1)² + (p_y2 - p_y1)² + (p_z2 - p_z1)²

What is the difference between displacement and distance? Distance is a scalar quantity that describes the length of the path traveled when changing position, and displacement is the vector that describes the difference between the starting and ending position. For example, if a 400-m runner ends a race exactly where he began, the displacement will equal zero, while the distance will equal 400 m. The difference between displacement and distance may be large or small, depending upon the circumstance.

Velocity (v): a change in position divided by a change in time or, v = (d)/(t₂ -t₁), described in m/s

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

Acceleration (a): a change in velocity divided by a change in time or, a = (v₂ - v₁)/(t₂ - t₁), described in m/s/s; remember that acceleration does not always indicate direction of travel.

The following shot put data demonstrate a graphical way to think of the relationship between position, displacement, velocity, and acceleration:

Position-Time Data

Velocity-Time Data

Another illustration of the relationship between velocity and acceleration: two more plots

Average and Instantaneous Measures of Velocity and Acceleration

Often, within a biomechanical context, it is important to distinguish between instantaneous and average measures of velocity and acceleration. Examples: cycling and sprinting.

Average cycling speeds

Instantaneous cycling speeds

Sprinting data

Part II: Projectile Motion

Notes from the powerpoint presentation regarding projectile motion.

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

Two projectile motion practice problems...

Practice Question:
Initial Velocity of Projectile

Answers:

Flight Time = 2.04 s

Maximum Height = 5.1 m

Horizotal Displacement = 10.2 m