AP Physics 1 Exam - 10 Tactical Hacks

Hack 1: Solve Every Question in Under 90 Seconds

• Core Thesis: Aim for under 90 seconds per question.
• If it takes longer, you're likely not using the most efficient method.
• Goal: Optimize your approach to solve questions in under 60 seconds.

Hack 2: Skip Long Text Walls

• Reading takes up a lot of time.
• Go to the last line to identify what you need to solve for.
• Options:
  • Derive an equation immediately.
  • Read the text with a specific intention.
• Example: Question regarding the magnitude of the angular momentum.
  • $L = Iω$
  • Conservation of angular momentum: $L<em>i = L</em>f$

Hack 3: Find the Hidden Equation/Law

• Every question, even conceptual ones, has a related equation or law.
• Aim to identify the equation within 20-25 seconds.
• You don't need the right equation, just a starting point.
• Example Problem: Two blocks colliding.
  • Identify: Collision implies conservation of momentum.
  • $P<em>i = P</em>f$
  • $m<em>A * v</em>A = (m<em>A + m</em>B) * v_f$
• Simplification:
  • Cancel out initial velocity, multiply by three, and subtract $m<em>A$ from both sides: $2m</em>A = m_B$
  • Conclusion: Mass of block B is twice the mass of block A.

Hack 4: Derive or Die Trying

• Avoid immediately plugging numbers; derive the equation first.
• Trust algebra over your calculator.
• Example Problem: Block A slides down and collides with Block B.
  • Collision implies conservation of momentum.
    • $P<em>i = P</em>f$
    • $m<em>A * v</em>A = (m<em>A + m</em>B) * v_f$
    • Missing: $v_A$
  • Derive $v_A$ using conservation of energy or kinematics. Energy is generally easier.
    • $E<em>i = E</em>f$
    • $mgh = frac{1}{2}mv^2$
    • $v = qrt{2gh}$
  • Plug $v$ into momentum equation:
    • $m<em>A* qrt{2gh} = (m</em>A + m<em>B) * v</em>f$
• Math is typically simple; the focus is on derivation.
• Example 2: Apple falling with air resistance.
  • Percentage of energy lost: $frac{E<em>lost}{E</em>initial} * 100$
    • $E<em>lost = E</em>i - E_f$
    • Simplified: $1 - frac{E<em>f}{E</em>i}$
  • Initial energy: Potential Energy
  • Final energy: Kinetic Energy
  • $1 - frac{ frac{1}{2}mv^2}{mgh}$
  • $1 - frac{v^2}{2gh}$

Hack 5: Interpret Diagrams First

• Understand diagrams to avoid reading unnecessary text.
• Skip to the last part of the question.
• Example Problem: Ball colliding with a rod.
  • Diagram implies conservation of angular momentum.
    • $L<em>i = L</em>f$
  • Asking for angular momentum of the rod.
    • $L = Iω$
  • If direct calculation isn't possible, return to conservation of momentum.
  • $P<em>i * d = P</em>f * d$

Hack 6: Graphs are Freebies

• Interpret graph before reading the question.

• Find the slope or area under the curve and determine its meaning.

• Example 1:

  • Force vs. Time graph. Area under the curve is impulse.

    • Impulse $= F * t = mΔv$

    • Look for change in speed ($Δv$).

    • $Δv = frac{Impulse}{m}$

  • Calculate the area of the curve: area = 500

    • Δv = 500 / 4000
    • Δv = .125

• Example 2:

  • Force vs Position: Area under the curve is Work/Energy
    • Solve problems using Work-Energy and derive formulas

Hack 7: Write Out All Variants of Equations

• Especially for Work-Energy and Impulse-Momentum.
• Example Problem: What is the change in angular momentum of the wheel?
  • Write out variants of $ΔL$: $L<em>f - L</em>i$, $I * Δω$, $torque * time$
• Look for variables within those variants while reading.
• If torque and time are given, use $ΔL = torque * time$

Hack 8: Use Conservation of Energy

• If you see an energy question, but are struggling to start solving use conservation of energy.
• Example problem: Runner colliding with a rope.
  • $E<em>i = E</em>f$
  • $frac{1}{2}mv^2=mgh$
    • Solving the equation for height shows that it is proportional to only velocity and gravity.
    • Height will therefore be the same for both.

Hack 10: Proportional Analysis

• Solve for relative values instead of specific values.
• College Board loves these types of questions.
• Example:
  • A newly discovered planet is found to have a density that's 2/3 that of planet Earth and a radius of two times as big as Earth. The surface gravitational field of the planet is most nearly…
  • Formula for gravitational field is: $G = frac{capital G * mass of the planet}{(radius of the planet)^2}$
  • Density is $p = mass/volume, therefore, mass = p * volume$
    • $G = frac{(capital G * p * V)}{R^2}$
  • $Volume = ( frac{4}{3})* π*R^3$
  • $G = frac{(capital G * p * ( frac{4}{3})πR^3)}{R^2}$ Simplify to:
    • $G/ (ρ * R) = constant$
  • G is directly proportional to $ρ * R$
  • Radius doubles but density decreases by 2/3rds, therefore G increases by 4/3s.

Hack 11: Center of Mass Remains Constant

• Position and velocity of the center of mass remain the same without external forces.
• If nothing is pushing from outside the system, motion/position doesn't change.
• Example 1: Person on a raft.
  • The person walks from one side of the raft to the other.
    • The raft must move to keep the center of mass in the same place.
• Example 2: Blocks connected by a spring.
  • The system is moving at 2 m/s.
  • The spring is released, causing the blocks to move apart.
    • Because there are no external forces the center of mass will still be moving 2m/s.