AP Physics C: Mechanics Notes

Kinematics Review (Mechanics)

Key Concepts

  • Dimensions

    • Importance of units in conversion and in final answers.

  • Vector vs. Scalar

    • Vectors: Quantities having both magnitude and direction.

    • Scalars: Quantities with magnitude only (can be positive or negative).

  • Velocity

    • Instantaneous Velocity: Derivative of position with respect to time. Not to be confused with average velocity.

    • Equation: v(t)=racdxdtv(t) = rac{dx}{dt}

    • Average Velocity: Total displacement divided by total time.

  • Acceleration

    • Instantaneous Acceleration: Derivative of velocity with respect to time. Not to be confused with average acceleration.

    • Equation: a(t)=racdvdta(t) = rac{dv}{dt}

  • Uniformly Accelerated Motion (UAM)

    • Equations for UAM include:

    • vx=vx0+axtv_x = v_{x_0} + a_x t

    • x=x0+vx0t+rac12axt2x = x_0 + v_{x_0} t + rac{1}{2} a_x t^2

    • rianglex=vit+rac12at2riangle x = v_i t + rac{1}{2} a t^2

    • vx2=vx02+2ax(x−x0)v_x^2 = v_{x_0}^2 + 2 a_x (x - x_0)

    • Important to note that ti=0t_i = 0 for these equations.

  • Free Fall

    • Described as motion where gravity is the only force acting on the object.

    • Acceleration due to gravity: ay=−g=−9.81extm/s2a_y = -g = -9.81 ext{ m/s}^2

    • Results in uniform motion with known acceleration downward.

Graphical Representations

  • Graphs of Free Fall:

    • Depict motion characteristics at a height of 2.0 meters.

Component Vectors

  • Definition: Vectors along x, y, (and z if applicable) directions.

  • Unit Vectors: Vectors of magnitude 1 in respective directions.

    • Example:
      extAccelerationinunitvectorform=axextextbfi+ayextextbfjext{Acceleration in unit vector form} = a x ext{ } extbf{i} + a y ext{ } extbf{j}

  • Vector Addition: Demonstrated through unit vectors simplifies calculations.

    • Example of position vector:

    • extbfr=−2.0extbfi+7.4extbfj−3.7extbfkextbf{r} = -2.0 extbf{i} + 7.4 extbf{j} - 3.7 extbf{k}

Relative Velocity

  • Definition: Based on vector addition.

    • Velocity of one object concerning another is the sum of their respective velocities.

    • Visualize with tip-to-tail representation of vectors.

Projectile Motion

  • Definition: Motion where an object travels under the influence of gravity acting in the vertical direction, while moving horizontally.

  • Characteristics:

    • Time interval riangletriangle t is the same for both x and y directions.

    • Break down initial velocity into components for calculation.

    • Example breakdown:

      • a=2.5extm/s2@26ext°EofNa = 2.5 ext{ m/s}^2 @ 26^ ext{°} E of N

      • ax=aextsin(heta)a_x = a ext{sin}( heta)

      • ay=aextcos(heta)a_y = a ext{cos}( heta)

      • Results:

      • axextext≈1.1extm/s2extextwithunitvectoria_x ext{ } ext{≈} 1.1 ext{ m/s}^2 ext{ } ext{with unit vector i}

      • ayextext≈2.2extm/s2extextwithunitvectorja_y ext{ } ext{≈} 2.2 ext{ m/s}^2 ext{ } ext{with unit vector j}

Dynamics Review (Mechanics)

  • Newton's Laws of Motion

    • Newton's 1st Law: An object at rest remains at rest, and an object in motion maintains its velocity unless acted upon by a net external force.

    • Inertial Reference Frame: Acceleration equals zero.

    • Non-Inertial Reference Frame: Accelerated frame.

    • Newton's 2nd Law: F=maF = ma or racdextbfpdt=extbfFextnetrac{d extbf{p}}{dt} = extbf{F}^{ ext{net}}

    • Newton's 3rd Law: For every action, there is an equal and opposite reaction.

Types of Forces

  • Force of Gravity (Weight)

    • Caused by the mass of an object and the gravitational field strength.

    • Fg=mgF_g = mg

    • Acceleration due to gravity at Earth’s surface: g=+9.81extm/s2g = +9.81 ext{ m/s}^2

  • Normal Force

    • Perpendicular force exerted by a surface against an object resting on it.

  • Tension Force

    • Force transmitted through ropes or strings that pull the connected object in the direction of the rope.

  • Applied Force

    • Push or pull exerted by one object on another.

  • Friction Force

    • Opposes the motion of two surfaces sliding past each other; dependent on types of surfaces in contact.

    • Static and kinetic friction distinguished between objects at rest and in motion.

Forces Summation and Free Body Diagrams

  • Free Body Diagram: Visual representations of the forces acting on an object.

    • Five Steps to Draw:

    1. Draw the free body diagram of each object.

    2. Break forces into components.

    3. Redraw the free body diagram.

    4. Sum the forces.

    5. Sum forces perpendicular to the forces from Step 4.

    • Must visually communicate the directions and magnitudes of forces involved.

Translational Equilibrium

  • Definition: When the net force acting on an object is zero.

    • No acceleration implies that the object is either at rest or moving with constant velocity.

Drag Force and Terminal Velocity

  • Drag Force: Opposes motion through a fluid or gas (resistive force).

    • Small objects moving slowly experience a proportional negative velocity drag.

    • The drag equation becomes complex when not at lower speeds.

  • Terminal Velocity: When the object reaches equilibrium during free fall under drag, extF<em>extdrag=extF</em>extgravityext{F}<em>{ ext{drag}} = ext{F}</em>{ ext{gravity}}.