Notes on Forces and Translational Dynamics from AP Physics 1 Review

Focus: Newton's Laws, forces, center of mass.

Center of Mass (CM):

• Equation: $x<em>{cm} = \frac{\sum (m</em>i \cdot x<em>i)}{\sum m</em>i}$

• Can be applied for any coordinate (y, z); measurements are relative to a reference point.

• For constant density objects, CM can be treated as collections of particles. Examples: Sphere, rectangular block, roll of tape, estimation for irregular shapes.

Forces:

• Forces are vectors with magnitude and direction arising from interactions.

• Free-Body Diagrams (FBD): Show all forces acting on an object with arrows starting at CM.

• Types: Normal force (perpendicular, outward), tension (uniform), contact forces (e.g., friction, applied force).

Newton's Laws:

1. First Law: An object at rest or in uniform motion stays that way unless acted upon (Law of Inertia).

2. Second Law: $F_{net} = m \cdot a$ ; direction matters, units: newtons (1 N = 1 kg·m/s²).

3. Third Law: For every action, there's an equal and opposite reaction.

Translational Equilibrium:

• Net force = 0; object is at rest or constant velocity.

Frictional Forces:

• Direction opposes motion, acts parallel to the surface.

• Magnitude: $F<em>{friction} \leq \mu \cdot F</em>{normal}$

• Kinetic Friction: $F<em>{kinetic} = \mu</em>k \cdot F<em>{normal}$ ; Static Friction: $F</em>{static} \leq \mu<em>s \cdot F</em>{normal}$ .

Applications in Free-Body Diagrams:

• Identify forces based on the situation (e.g., book against wall). Components of gravity on incline: $F<em>{g{perpendicular}} = mg \cos(\theta)$ , $F</em>{g{parallel}} = mg \sin(\theta)$ .

Conclusion:

• Mastering forces, CM, and Newton's Laws is essential for physics dynamics problems, complemented by practice with FBDs.