KNES 361 L4

Angular Kinematics

Overview of Motion Types

• Two types of motions: linear and angular.

  • Linear Motion: The motion of an object in a straight line.

  • Example: A car moving in a straight line from one point to another.

  • Angular Motion: The rotational motion around an axis.

  • Example: The wheels of the car rotating around their axis.

Characteristics of Angular Motion

• Angular motion occurs in a plane around an axis of rotation.

• The plane and axis are always perpendicular to each other, with no exceptions.

  • Example: Lifting an arm involves rotating around the shoulder joint axis in a specific plane.

• Different body parts experience different types of motion simultaneously:

  • E.g., in a spin, the shoulder joint and hand move through the same angle, but the head covers a different distance than the shoulder.

Importance of Angular Motion

• Many everyday movements in sports involve rotation around joints.

  • Examples: Swinging a racket, walking.

• Understanding angular motion aids various professionals such as coaches, clinicians, and physical therapists to optimize performance and minimize injuries.

• Movements usually occur in diagonal planes rather than cardinal planes.

  • Understanding cardinal planes is important for understanding diagonal planes.

Angular Kinematics

• Angular kinematics studies motion without considering forces, focusing instead on the appearance and speed of motion.

• Basic concepts apply:

  • Displacement, velocity, acceleration can all be translated to angular motion around an axis.

Angular Position

• Basic measure of angular motion; other measurements derive from it.

• Types of Angular Position:

  1. Absolute Angular Position: Measured relative to a fixed plane or line that does not move with respect to the Earth.

     • Example: Elbow, hip, knee, and ankle angles measured from a horizontal line.

  2. Relative Angular Position: Measured between two moving lines or planes.

     • Example: The elbow angle between the forearm and upper arm changes as both move.

Angular Displacement

• Change in angular position; can be calculated from angular position.

  • Formula: $heta<em>{disp} = heta</em>{final} - heta_{initial}$

  • Example: In a biceps curl, moving from 90 degrees flexion to straight elbow position results in angular displacement.

• Measurement: In degrees, radians, or revolutions.

• Angular displacement is a vector quantity, which depends on direction:

  • Counterclockwise movement is positive; clockwise movement is negative.

Angular Distance

• The sum of all angular changes during motion, regardless of direction.

  • Example: A pendulum swinging left to right is summed up to calculate angular distance.

• Angular displacement vs. angular distance:

  • Angular displacement: Ending position minus starting position.

  • Angular distance: Total angle traveled.

Units of Measurement

• Angular Position, Distance & Displacement: Measured in revolutions, degrees, or radians.

  • 1 revolution = 360 degrees = 2π radians.

  • Half revolution = 180 degrees = π radians.

  • Quarter revolution = 90 degrees = π/2 radians.

  • Three-fourth revolution = 270 degrees = 3π/2 radians.

Examples of Angular Displacement and Distance Calculation

• Biceps Curl:

  • Initial position = 90 degrees, final position = 180 degrees.

  • Angular Displacement: $180^{ ext{o}} - 90^{ ext{o}} = 90^{ ext{o}}$

  • Angular Distance: 90 degrees (in a single direction).

• Returning to Original Position:

  • Moving from 90 degrees to 180 degrees (displacement = 90 degrees) and then back to 90 degrees results in:

  • Angular Displacement = 0 degrees (back to original).

  • Angular Distance = 90 degrees + 90 degrees = 180 degrees.

Angular Velocity

• Definition: The rate of change of angular position.

• Formula: $ext{Angular Velocity} ( ext{ω}) = rac{ ext{Change in Angular Position} ( heta)}{ ext{Change in Time} ( ext{Δt})}$

  • Units: degrees/second, radians/second, revolutions/second or revolutions/minute.

Examples of Angular Velocity Calculation

• Clock Example:

  • Second hand completes 1 revolution (360 degrees) in 60 seconds.

  • $ext{Angular Velocity} = rac{360^{ ext{o}}}{60 ext{s}} = 6^{ ext{o}/ ext{s}}$

• Gymnast Example:

  • One somersault in 0.9 seconds.

  • $heta = 360^{ ext{o}}, ext{Δt} = 0.9 ext{s}$

  • $ext{Angular Velocity} = rac{360^{ ext{o}}}{0.9 ext{s}} = 400^{ ext{o}/ ext{s}}$

Average Angular Velocity

• Formula: $ext{Average Angular Velocity} = rac{ ext{Final Position} - ext{Initial Position}}{ ext{Total Time}}$

Angular Acceleration

• Definition: The rate of change in angular velocity.

• Formula: $ext{Angular Acceleration} ( ext{α}) = rac{ ext{Final Angular Velocity} - ext{Initial Angular Velocity}}{ ext{Time}}$

  • Units: degrees/second², radians/second², or revolutions/second².

Examples of Average Angular Acceleration

• Given angular velocities at different time points:

  • Start: 0º/s, at 0.5 s: 100º/s, at 1 s: 250º/s.

  • Calculates average angular acceleration over 1 s using the formula.

  • $ext{α} = rac{250^{ ext{o}/ ext{s}} - 0^{ ext{o}/ ext{s}}}{1 ext{s}} = 250^{ ext{o}/ ext{s}^{2}}$

Relationship Between Linear and Angular Motion

• Key Concept: The greater the distance from the axis of rotation, the greater the linear distance travelled during rotation.

  • Example: Different parts of a spinning baseball bat travel at different distances; points further from the axis travel further.

  • In gymnastics, feet (further from axis) travel greater distance than hands (closer to axis).

• This knowledge is critical for understanding the biomechanics of movements like throwing and jumping.

Conclusion

• Overview of angular motion, kinematics, and the distinction from linear motion.