Lecture Notes: Angular Momentum, Impulse, and Newton's Laws

Introduction

• Reaction board math is on the worksheet and lab, but not on the exam.
• Review of conservation of angular momentum: changes in radius of gyration affect moment of inertia and angular velocity.

Angular Momentum and Cats' Righting Reflex

• Conservation of angular momentum is consistent across scenarios.
• Cats' ability to land on their feet showcases angular momentum principles:
  • Flexible spine creates upper and lower body segments with separate axes of rotation.
  • Upper body orientation prioritized by tucking front legs and extending back legs to increase angular velocity.
  • Process repeated until cats land on feet.

Angular Impulse and Momentum Relationship

• Linear impulse: force over time.
• Angular impulse: torque over time, measured in Newton meter seconds.
• Angular impulse changes an object's angular momentum.

Math Examples

• Heavy math lecture with practice problems.
• Example Problem 1: Calculate torque required for hip flexors to achieve leg angular velocity of 3.5 radians/s in 0.2 seconds.
• Example Problem 2: Calculate torque needed for hip extensors to stop leg rotation in 0.4 seconds.

Angular Work and Power

• Joint work: torque x angular displacement, measured in joules/Newton meters.
• Joint work can be positive (same direction of joint moment and displacement) or negative (opposite directions).
• Angular or joint power: product of torque and angular velocity, measured in watts.
• Positive power associated with power generation; negative power with energy absorption.

Application in Sports

• Understanding of joint power essential for sports performance and rehabilitation.
• Importance in training trunk and pelvis rotational power for baseball pitchers.

Newton's Laws Translated to Angular Motion

• First Law: Rotating bodies remain in constant rotation unless external torque is applied.
• Second Law: Net torque causes angular acceleration proportional to magnitude and direction of torque.
• Third Law: For every applied torque, there is an equal and opposite reaction torque.

Practice Problem: Newton’s Second Law (Angular)

• Calculate force needed by quadriceps for knee joint angular acceleration given known variables.
• Consider angle of pull in calculations.

Contralateral Motion

• Importance of contralateral arm and leg movement in walking/running to balance torques.
• Example of baseball hitting: upper and lower body apply opposite reaction torques.

Wrap-up

• Review of topics: angular work, power, Newton's angular laws, and problem-solving with torque.

Key Topics to Study:

• Conservation of angular momentum and its practical examples.
• Angular impulse-momentum relationship.
• Solving angular motion problems using given variables.
• Angular work and power concepts.
• Application of Newton’s laws in an angular context.