AP Physics 1 Key Concepts

Unit 1: Kinematics

• Kinematics Overview

  • Vectors: quantities that have both magnitude and direction.

  • Scalars: quantities that have only magnitude.

• Distance and Displacement

  • Distance: length of the path taken between initial and final position (scalar).

  • Displacement: straight-line distance from initial to final position, defined as:
    \text{Displacement} = \text{Final Position} - \text{Initial Position} (vector).

  • Relationship: Distance is always greater than or equal to the magnitude of displacement.

• Velocity and Acceleration

  • Average Velocity: defined by the equation:
    \text{Average Velocity} = \frac{\text{Displacement}}{\Delta t} (vector).

  • Average Acceleration: defined by the equation:
    \text{Average Acceleration} = \frac{\Delta v}{\Delta t} (vector).

  • Instantaneous Velocity/Acceleration: values at a specific time interval.

• Uniformly Accelerated Motion (UAM)

  • Conditions: Constant acceleration allows use of the kinematics equations.

  • Kinematics Equations (5 variables, 4 equations): Knowing 3 variables lets you solve for the other 2.

• Graph Interpretation

  • Slope of position vs. time graph = velocity.

  • Slope of velocity vs. time graph = acceleration.

  • Area under velocity vs. time graph = change in position.

  • Area under acceleration vs. time graph = change in velocity.

  • Areas above x-axis are positive, below are negative.

• Vector Resolution

  • Break vectors into components using sine and cosine functions.

  • Note: The angle ( \theta ) may not always be from the horizontal.

• Projectile Motion

  • Governed only by gravitational force near Earth's surface.

  • Acceleration in y-direction: 9.81 m/s² (use 10 m/s² for problems).

  • In x-direction: constant velocity, zero acceleration.

  • Importance of frame of reference in relative motion calculations.

Unit 2: Force and Translational Dynamics

• Center of Mass

  • Formula:

    Center of Mass=∑mi​∑(mi⋅xi)​

  • Calculates the average position of a system's mass distribution, reflecting how the system behaves under the influence of external forces.

  • Valid when replacing position with velocity or acceleration.

• Forces as Vectors

  • All forces result from interaction between two objects.

  • Free Body Diagrams: Show all forces acting on an object, starting from center of mass.

    • Do not decompose force vectors in free body diagrams.

• Newton's Laws

  • First Law: An object at rest will remain at rest, and an object in motion will remain in motion unless acted upon by a net force (law of inertia).

  • Second Law:
    \text{Net Force} = m \cdot a
    (where both are vectors).

  • Third Law: For every action, there is an equal and opposite reaction.

Unit 3: Work, Energy, and Power

• Energy Principles

  • Kinetic Energy:
    KE = \frac{1}{2} m v^2

  • Work:
    W = F \cdot d \cdot \cos(\theta)

  • Work done by conservative forces = independent of path.

  • Examples of conservative forces: gravitational force, spring force.

  • Potential Energy:

  • Gravitational:
    PE = mgh

  • Elastic:
    PE = \frac{1}{2} k x^2

• Mechanical Energy Conservation

  • Total mechanical energy remains constant if no net work is done on the system by nonconservative forces.

  • Work-Energy Principle:
    W_{net} = \Delta KE

• Power

  • Rate of work done:
    P = \frac{W}{\Delta t}

  • Instantaneous power:
    P = F \cdot v \cdot \cos(\theta)

Unit 4: Linear Momentum

• Momentum:

  • Linear momentum:
    p = mv

  • Impulse:
    J = \Delta p = F_{avg} \cdot \Delta t

  • Conservation of Momentum:

  • In collisions, momentum before equals momentum after (when net external force is negligible).

• Types of Collisions

  • Elastic: Total kinetic energy is conserved.

  • Inelastic: Total kinetic energy decreases.

  • Perfectly Inelastic: Objects stick together post-collision.

Unit 5: Torque and Rotational Dynamics

• Torque:

  • Defined as:
    \tau = r \cdot F \cdot \sin(\theta)

  • Lever arm (perpendicular distance): Important for calculating torque.

• Newton's Laws in Rotation

  • First Law: An object in rotational equilibrium will remain in that state unless acted upon by a net external torque.

  • Second Law:
    \text{Net Torque} = I \cdot \alpha

Unit 6: Energy and Momentum of Rotating Systems

• Rotational Energy

  • Rotational Kinetic Energy:
    KE_{rot} = \frac{1}{2} I \omega^2

  • Total energy: Sum of translational and rotational energies.

• Rolling Motion

  • Describes motion of rigid bodies: Must consider both translational and rotational kinetic energy.

  • Equations for rolling without slipping: Similar to those for circular motion.

Unit 7: Oscillations

• Simple Harmonic Motion (SHM)

  • Restoring force is proportional to displacement from equilibrium position.

  • Period (T) and amplitude (A) defined for oscillating systems.

  • Key equations for SHM in mass-spring and pendulum systems.

• Energy in SHM

  • Total mechanical energy remains constant throughout the oscillation.

Unit 8: Fluids

• Fluid Properties

  • Density:
    \rho = \frac{m}{V}

  • Pressure:
    P = \frac{F}{A}

  • Absolute pressure accounts for fluid depth and weight.

• Fluids in Motion

  • Continuity Equation:
    A1v1=A2v2

  • Bernoulli's Equation for ideal fluid flow.

  • Torricelli’s theorem for speed of fluid exiting a hole.