Biomechanics: Degrees of Freedom, Mass vs. Moment of Inertia, and Equations of Motion

Definition: Degrees of freedom represent all the free and independent ways a system can move.
Examples:
- Human Body: Has numerous degrees of freedom. A finger joint can move independently of other joints, and the neck can move in various independent directions.
- Simple Pinned Model (e.g., a bat pinned to the ground): This model has only one degree of freedom. It can only rotate about the pinned axis. Any upward/downward or forward/backward motion of the bat's center of mass is not an independent degree of freedom because these motions are coupled to the rotation. The bat cannot move vertically or horizontally anywhere it wants; its vertical and horizontal positions are determined by its rotational angle. This coupling means they are not independent ways of motion.
Importance: Identifying degrees of freedom is crucial for applying Newton's laws in free body diagrams. Laws of physics are applied at these degrees of freedom because they represent the only ways the system can move independently.

Mass (m):
- Represents resistance to translation (linear motion).
- Example: It's harder to lift a $200\text{ lb}$ barbell than a $100\text{ lb}$ barbell because the heavier one has more mass and thus more resistance to being translated.
- Every body has a single, set value of mass (though it can change if material is added or removed).
Moment of Inertia (I) / Angular Mass:
- Represents resistance to rotation (angular motion).
- Preferred Term: The instructor prefers