Objectives:

• Define:
  • Relative and absolute angular position
  • Angular displacement
  • Average angular velocity
  • Instantaneous angular velocity
  • Average angular acceleration
  • Instantaneous angular acceleration
• Name units of measurement for above definitions
• Explain the relationship between angular and linear motion
• Define:
  • Tangential acceleration and explain its relationship to angular acceleration
  • Centripetal acceleration and explain its relationship to angular velocity and tangential velocity
• Describe anatomical position
• Describe the three principal anatomical planes and axes
• Describe the joint actions that occur at each of the major joints

What is angular kinematics?

What is an angle?

θ = arc length/r

Degrees and Radians
 

Common conversions: 180 ° = 3.14 radians, or, I prefer: 57.3 ° = 1 radian

How do we use absolute and relative angles to describe anatomical systems?

The relationship between Linear and Angular Kinematics

Exactly as was the case for linear kinematics, the slope of angular position versus time equals angular velocity
Running Example

Relationship Between Linear and Angular Distances:

d = Ө * r  

Practice: If a 34 inch baseball bat rotates 180 degrees how far has the sweet spot traveled (Assume that the sweet spot is 31 inches from the axis of rotation)?

Relationship Between Linear and Angular Velocity: Baseball bat example

V = w * r

Practice: If bat is swung through the aforementioned arc in 0.4 seconds, what was the linear velocity? What was the angular velocity?

Another Application: If you want to increase v for a rotating object, you can increase ω or r. If you are playing golf, the likely choice is to increase r. The typical length of a 3-iron is 38.5 inches, and each club, from the 3-iron to the wedge, decreases in length by 1/2 inch. With this in mind, how might performance in other sports be increased by increasing r?

Angular Acceleration

Resolving Angular Acceleration into Two Orthogonal, Linear Components

Tangential Acceleration: The component of of linear acceleration tangent to the circular path of a point on a rotating object; this is the component of angular acceleration that influences the linear speed of the object

a_T = a * r

Centripetal Acceleration: The linear acceleration directed toward the axis of rotation; this is the component of angular acceleration that influences the direction of the object

a_r = w ² r, or

a_r = v²/r

Anatomical Systems for Describing Limb Movements:

Before you describe limb movements, you should be familiar with the anatomy of the human musculoskeletal system.

The body segments you should be familiar with (for the context of this class) are:

The bones you should be familiar with (for the context of this class) are: Image

For the context of this class, the muscles, and muscle functions, you should be familiar with are (those muscles that are circled): Muscles

When describing motion, the anatomical position is helpful. The anatomical position is the standard reference position for the body when describing locations position, or movements of limbs or other anatomical structures.

 

Spatial and directional terminology to be familiar with:
 

Anterior/Posterior
Superior/Inferior
Medial/Lateral
Proximal/Distal

Sagittal Plane--Frontal, or Meidal-lateral Axis

Frontal Plane--Sagittal, or Anterior-posterior Axis
Transverse Plane--Longitudinal (Long) Axis

Joint Actions

Sagittal Plane
 

Flexion, extension, hyperextension, dorsiflexion, and plantar flexion

Frontal Plane

Adduction, abduction, radial deviation, ulnar deviation, eversion, inversion, and lateral flexion

Tranverse Plane

Rotation, horizontal abduction and adduction, and forearm supination and pronation

Other joint actions to know:

Scapular motion: elevation/depression, and upward (lateral boarder moves up)/downward (lateral boarder moves down) rotation

Circumduction: multiple axis joint action

Pronation (subtalar joint): a combination of dorsiflexion, eversion, and abduction

Supination (subtalar joint): a combination of plantarflexion, inversion, and adduction

 

An exercise in describing human motion.

Summary

1. Angular kinematics is the description of angular motion.

2. Angles describe the orientation of two lines; these angles can be absolute or relative.

3. Three cardinal planes (sagittal, frontal, and transverse) and three cardinal axes (medial-lateral, anterior-posterior, and longitudinal) are helpful in describing linear and angular motion.

4. When an object, including a body segment, rotates, it undergoes angular displacement.

5. Angular displacement, angular velocity, and angular acceleration are each similar to their linear counterparts.

6. Linear displacement, velocity, and acceleration are: 1) dependent upon their angular counterparts, reported in radians, and 2) related to the length of the radius.

7. Lengthening the radius without decreasing angular velocity is important in a variety of sports (e.g. tennis, baseball, and golf).

8. Radial, or centripetal, acceleration is the component of angular acceleration that is directed towards the middle of the curvature. Radial acceleration is directly proportional to the square of the tangential linear velocity of the square of the angular velocity.

Chapter Six Sample Exam Questions

Solutions