AP Physics 1: Unit 2 Review - Forces and Translational Dynamics

Newton’s Laws, Forces, and Center of Mass

Center of Mass

• Equation for Center of Mass of Particles
  • ( x_{cm} = \frac{\sum m_i x_i}{\sum m_i} )
  • Can be applied in x, y, or z directions, depending on the problem.
  • Position is relative to a zero point, which could be the origin or another defined point.
• Application
  • Also used to determine velocity or acceleration by replacing position with velocity or acceleration in the equation.

Center of Mass of Objects with Shape

• Treated as a collection of particles with little interaction.
• Constant Density Objects
  • Sphere: Center of mass at geometric center.
  • Rectangular Block: Center of mass at geometric center.
  • Roll of Tape: Center of mass at geometric center.
  • Banana: Approximate center of mass.
• Projectile Motion
  • Objects rotate around their center of mass following a parabolic arc.

Forces

Properties of Forces

• Forces are vectors with both magnitude and direction.
• Result from interactions between two objects.
• Free-Body Diagrams (FBDs)
  • Show all forces acting on an object.
  • Only include force vectors, not displacement, velocity, etc.
  • All force arrows originate from the center of mass.

Steps to Solve Free-Body Diagram Problems

1. Draw the free-body diagram.
2. Break forces into components.
3. Redraw the diagram.
4. Sum the forces in one direction.
5. Sum the forces in the perpendicular direction.

Types of Forces

• Normal Force
  • Perpendicular to surface, pushes away.
• Tension
  • In ropes, cables, strings; parallel to the direction of the rope.
• Newton’s Laws
  • First Law (Inertia): An object remains at rest or at constant velocity unless acted upon by a net, external force.
  • Second Law: ( F_{net} = ma ), where force and acceleration are vectors.
  • Third Law: For every action, there is an equal and opposite reaction.

Gravitational Force

• Between two masses; magnitude given by ( F_{gravity} = mg ).
• Direction is toward the center of mass of the planet.

Friction

• Static Friction: Adjusts to prevent motion until maximum threshold.
• Kinetic Friction: When surfaces slide relative to each other.
• Coefficient of Friction
  • No units, usually between 0 and 2.
  • Experimental value depending on surface roughness.

Translational Equilibrium

• Net force on an object is zero, leading to constant velocity or rest.

Free-Body Diagram Example

• Forces on a book against a wall: applied force, gravity, normal force, static friction.
• Newton's Third Law Pairs
  • Forces act in pairs between two objects, not on the same object.

Inclined Planes

• Break force of gravity into components: parallel and perpendicular to the incline.
• Equations
  • Gravity parallel: ( mg \sin(\theta) )
  • Gravity perpendicular: ( mg \cos(\theta) )