Angular Kinetics Lecture Notes

Overview

• Duration: 2-3 days, dependent on exam review progress
• Key Topics:
  • Center of Mass (COM) and Center of Gravity (COG)
  • Angular Momentum Impulse Relationship
  • Angular Work and Power
  • Angular Analogs of Newton's Laws

Center of Mass (COM)

• Definition: Location where mass is evenly distributed
• Uniform Density: COM is in the center if object density is uniform
• Non-uniform Density: COM shifts towards where there's more mass (e.g., baseball bat)
• Exams: Not required to visually determine COM or density
• Body Weight Vector: Originates at COM location

Center of Gravity (COG)

• Point: Same as COM
• Exams: Not specifically tested

Anatomical Considerations

• Human body is not of uniform density
• General Observations:
  • Potential more muscle mass on dominant side
  • More mass in lower than upper body
  • Back may have more mass than front
• Estimation: In anatomical position, COM is near the navel
• COM Movement: Shifts with body movement (e.g., raising arms)

Methods to Quantify COM

• Position: Measured in meters from feet
• Percentage: % of total height, more common
• Average percentages vary:
  • Women: ~54% of height
  • Men: ~57% of height

Estimating Techniques

• Segmentation Method
• Reaction Board Method
  • Components: 2 force plates, rigid board
  • Measurement: Static analysis of COM
  • Formulas: Sum of all torques = 0

Moment of Inertia (MOI)

• Definition: Resistance to change in angular acceleration
• Variables:
  • Mass (M)
  • Radius of Gyration (K)
• Formula: MOI = M * K²
  • K has the largest influence*

Sports Applications

• Baseball/Swinging: Donuts increase MOI, choking up reduces it
• Running: Swing leg dynamics, varied MOI through stride

Moment of Inertia in Rotation

• Examples:
  • Baseball bat with different donut placements
  • Bicep curls: Dumbbell vs. Kettlebell

Angular Momentum

• Definition: Quantity of angular motion
• Formula: H = MOI * Angular Velocity
• Conservation: Remains constant unless external torque applied*

Conservation of Angular Momentum

• Example: Figure skaters adjust arm/leg positions to control spin
• Angular momentum is conserved; MOI and Angular Velocity adjustments

Exam Preparation

• Topics to focus: Reaction board method, influence of MOI, conservation of angular momentum
• Upcoming slides and notes review recommended for next class

End of Lecture

• Questions and exam review to follow
• Students encouraged to stay for exam opening details