Lecture Notes on Angular Kinetics

Introduction to Angular Kinetics

• Understanding center of mass (COM), center of gravity
• Angular momentum-impulse relationship
• Angular work and power
• Angular analogs of Newton's laws of motion

Center of Mass (COM)

• Definition: Location on an object where mass is evenly distributed; depends on object density.
  • Uniform density: COM is in the middle.
  • Non-uniform density: COM shifts towards the heavier end.
• Applications:
  • Body weight/segment weight vectors start at the COM.
  • No need to know center of gravity for exams.
• Anatomical COM:
  • Not uniformly dense; estimated around the navel or intersection of three planes in anatomical position.
  • COM shifts with body mass alterations (e.g., raising arms).

Estimating COM

• Methods:
  • Position in meters or percentage of total height.
  • Biological differences in COM location (e.g., wider pelvis in women).
• Techniques:
  • Segmentation method (not covered in detail)
  • Reaction Board method (covered in lab, not tested on exam)
• Reaction Board:
  • Uses two force plates and a wooden board.
  • Calculates distance from foot to COM.

Moment of Inertia (MOI)

• Concept:
  • Angular counterpart to linear inertia; resistance to rotational acceleration.
  • MOI depends on mass distribution relative to axis of rotation.
• Mathematics:
  • Formula: I = MK^2 (moment of inertia = mass x radius of gyration squared)
  • Radius of gyration: Average distance of mass particles from axis (simplified to distance from axis to COM).
• Applications:
  • Choking up on a bat reduces MOI, eases swinging.
  • In activities like bicep curls, kettlebell curls feel harder due to greater MOI.

Angular Momentum

• Definition: Quantity of angular motion; H = MOI x angular velocity.
• Influence:
  • Radius of gyration is a major influence.
  • Conservation of angular momentum: Remains constant unless acted on by external torque.

Practical Applications

• Figure Skating:
  • Tucking arms/legs reduces MOI, increasing spin speed.
  • Extending arms/legs increases MOI, slowing down.
• Exam Tips:
  • Concepts like COM, MOI, and conservation of momentum are crucial.
  • Figure skating example likely on exam.

Conclusion

• Review notes and compare with the full version for better understanding.
• Exam preparation includes understanding concepts without heavy reliance on mathematical calculations.

These notes provide a comprehensive overview of the key points discussed in the lecture on angular kinetics. Be sure to understand the concepts and examples, as they are likely to be tested on the exam.