Lecture Notes: Angular Kinetics and Impulse

Reaction Board Math Clarification

• Not on the exam
• Important for worksheets and labs

Conservation of Angular Momentum

• Angular momentum is conserved in all situations.
• Can change radius of gyration to alter moment of inertia and angular velocity
• Example: Cat's Righting Reflex
  • Cats land on feet due to a flexible spine and segmented body rotation.
  • Upper body prioritized by tucking front legs, extending back legs.
  • Lower body follows by tucking back legs, extending front legs.

Impulse

• Linear impulse: Force over time
• Angular impulse: Torque over time
  • Formula: Torque x Time = change in Angular Momentum
  • Example: Torque applied to a ball changes its angular momentum.

Mathematics of Angular Impulse

• Practice problems involve calculating torque and force.
  • Example Problem: Calculating torque required by hip flexors to achieve leg angular velocity of 3.5 rad/s in 0.2 seconds.

Angular Work and Power

• Joint Work: Torque x Angular Displacement
  • Positive work: Joint moment and angular displacement same direction.
  • Negative work: Joint moment and angular displacement opposite direction.
• Joint Power: Torque x Angular Velocity
  • Positive power: Joint moment and velocity same direction.
  • Negative power: Joint moment and velocity opposite direction.
  • Example: Baseball pitching requires pelvis and trunk rotational power.

Newton’s Laws of Angular Motion

• First Law: A rotating body will continue to rotate unless an external torque is applied.
• Second Law: Net torque causes angular acceleration proportional to magnitude and direction of torque.
  • Formula: Torque = Moment of Inertia x Angular Acceleration (Torque = I x α)
• Third Law: For every applied torque, there's an equal and opposite reaction torque.
  • Examples include running arm-leg swing and baseball batting.

Practice Problems

• Solving torque and force using provided variables.
• Incorporating angle of pull in calculations.

Conclusion & Wrap-up

• Review of key concepts: Angular work, power, Newton’s laws, and calculation practice.
• Next topic: Tissue biomechanics.