AP Physics 1 Review Notes

Kinematics Review

• Distance: Total path traveled, scalar.

• Displacement: Straight line distance from start to end, vector, $∆𝑥 = 𝑥𝑓 − 𝑥 𝑜$.

• Speed: Scalar, $Distance / time$.

• Velocity: Vector, $Displacement / time = ∆𝑥 / 𝑡$.

• Acceleration: Change in velocity, vector, $𝑎 = ∆𝑣 / 𝑡𝑖𝑚𝑒$.

• Free Fall: Only gravity acts, $g = -9.8 m/s^2 ≈ 10 m/s^2$.

Graphs

• Position vs. Time:

  • Slope: Velocity.

  • Y-Value: Position.

• Velocity vs. Time:

  • Slope: Acceleration.

  • Area: Displacement.

  • Y-Value: Velocity.

Uniformly Accelerating Objects (UAM)

• Constant acceleration.

• Equations:

  • $𝑥 = 𝑥 𝑜 + 𝑣 𝑜 𝑡 + (1 / 2)𝑎𝑡^2$

  • $𝑣𝑓^2 = 𝑣 𝑜^2 + 2𝑎(𝑥 − 𝑥 𝑜)$

  • $𝑣𝑓 = 𝑣 𝑜 + 𝑎𝑡$

2D Kinematics

• Cliff Diver Style: Horizontal velocity with free fall.

• X-direction: Constant velocity.

• Y-direction: UAM.

Relative Motion

• Vector addition of components.

Center of Mass

• Represents object's motion.

• Closed system: Actions inside the system.

• Open system: External influences.

Forces Review

• Inertial Mass: Resists change in motion.

• Gravitational Mass: Attracted to other mass.

• Newton's First Law: Object at rest stays at rest, object in motion stays in motion unless acted upon by a net external force.

• Newton's Second Law: $\sum{𝐹} = 𝑚𝑎$ or $𝑎 = \frac{\sum{𝐹}}{𝑚}$

• Newton's Third Law: Equal and opposite reaction forces.

Common Forces

• Gravity:

  • On Earth: $Fg = W = mg$, where $g ≈ 10 m/s^2$

  • In space: $𝐹 𝑔 = \frac{𝐺𝑀𝑚}{𝑟^2}$, G = $6.674 \times 10^{-11}$

• Normal Force: Perpendicular to surface, a push.

• Applied Force: Force put on an object.

• Friction Force: $𝐹𝑓 = 𝐹 𝑁µ_{s,k}$, where µ is the coefficient of friction.

  • Static: Keeps objects still.

  • Kinetic: Sliding friction.

• Tension: Force caused by a rope, always a pull.

• Centripetal Force: Changes direction of motion, points towards the center, $𝐹 𝑐 = \frac{𝑚𝑣^2}{𝑟}$.

  • Satellites: $𝑣_{orbit} = \sqrt{\frac{GM}{r}}$; $T^2 = \frac{4π^2}{GM}R^3$

• Spring Force: $𝐹 𝑠 = −𝑘∆𝑥$

Energy Conservation

• Closed Systems: Energy, momentum, mass, and charge are conserved.

• Open Systems: Outside forces or energies act on it.

• Work: $𝑊𝑜𝑟𝑘 = 𝐹 |𝑑| = 𝐹𝑑𝑐𝑜𝑠θ$ (Joules).

• Kinetic Energy: $𝐾𝐸 = (1 / 2)𝑚𝑣^2$.

• $𝑊<em>{net} = ∆𝐾𝐸 = 𝐾𝐸</em>f − 𝐾𝐸<em>0 = (1 / 2)𝑚𝑣</em>f^2 − (1 / 2)𝑚𝑣_0^2$

• Potential Energy:

  • Elastic: $𝑈 𝑠 = (1 / 2)𝑘∆𝑥^2$

  • Gravitational:

    • Earth: $𝑈 𝑔 = 𝑚𝑔ℎ$

    • Space: $𝑈 𝑔 = -\frac{𝐺𝑀𝑚}{r}$

• Escape Velocity: $𝑣_{escape} = \sqrt{\frac{2𝐺𝑀}{r}}$

• Closed System: MEo=MEf; KEo+Ug,o+Us,o=KEf+Ug,f+Us,f

• Open system: MEo=MEf + Wfric

• Power: $𝑃 = \frac{∆𝐸}{𝑡} = \frac{𝑊𝑜𝑟𝑘}{𝑡}$ (Watts).

• Power (constant): $𝑃𝑜𝑤𝑒𝑟 = 𝐹 |𝑣𝑒𝑙|$

Momentum Conservation

• Momentum: $𝑝 = 𝑚𝑣$ (kg m/s).

• Impulse: $𝐽 = \sum{𝐹} · ∆𝑡 = ∆𝑝$ (kg m/s or N·sec).

• Elastic Collisions: Kinetic energy is conserved.

• Inelastic Collisions: Kinetic energy is not conserved.

• Perfectly Inelastic: Objects stick together after collision, $m<em>1v</em>{1,0} + m<em>2v</em>{2,0} = (m<em>1+ m</em>2)v_f$

• Explosion: $(m<em>1 + m</em>2)v<em>0 = m</em>1v<em>{1,f} + m</em>2v_{2,f}$

• Center of Mass: $𝑚<em>{tot}𝑟</em>{cm} = \sum m<em>i r</em>i$

Oscillations Review

• Simple Harmonic Motion (SHM): Restoring force without damping.

• Motion follows a sine/cosine curve: $𝑥 = 𝐴𝑐𝑜𝑠(2π𝑓𝑡)$.

• Frequency (f): Hz, $T = (1 / f)$.

• Mass Spring System: $T = 2π \sqrt{\frac{m}{k}}$

• Pendulum Motion: $T = 2π \sqrt{\frac{l}{g}}$

Fluids Review

• Fluid: Substance with free-moving atoms.

• Density: $ρ = \frac{𝑀𝑎𝑠𝑠}{𝑉𝑜𝑙𝑢𝑚𝑒}$.

• Specific Gravity: $𝑆𝑝𝑒𝑐 𝐺𝑟𝑎𝑣 = \frac{ρ<em>{object}}{ρ</em>{fluid}}$.

• Pressure: $𝑃𝑟𝑒𝑠𝑠 = \frac{𝐹 ⊥}{𝐴𝑟𝑒𝑎}$ (Pascals).

• Absolute Pressure: $𝑃 = 𝑃_{atm} + ρ𝑔ℎ$

• Gauge Pressure: $𝑃 𝑔 = ρ𝑔ℎ$

• Buoyant Force: $𝐹𝑏 = ρ(𝑉𝑜𝑙)𝑔$

• Rate(Q): $𝑅𝑎𝑡𝑒(𝑄) = \frac{𝑉𝑜𝑙}{𝑡} = 𝐴(𝑣𝑒𝑙)$

• Continuity equation: $𝐴 1𝑣𝑒𝑙1 = 𝐴 2𝑣𝑒𝑙2$

• Bernoulli’s: $𝑃 1 + ρ𝑔𝑦1 + (1 / 2)ρ𝑣1^2 = 𝑃 2 + ρ𝑔𝑦2 + (1 / 2)ρ𝑣2^2$

• Torricelli’s Theorem: $𝑣 = \sqrt{2𝑔∆𝑦}$

Rotations Review

• Angular Displacement: θ (radians).

• Angular Velocity: ω (rad/s).

• Angular Acceleration: α (rad/s2).

Translational to Angular Relationships:

• $∆𝑥 = 𝑟 · ∆θ$

• $𝑣 = 𝑟 · ω$

• $𝑎 = 𝑟 · α$

• Uniformly Accelerating Motion:

  • $θ = θ<em>0 + ω</em>0𝑡 + (1 / 2)α𝑡^2$

  • $ω<em>𝑓^2 = ω</em>0^2 + 2α∆θ$

  • $ω<em>𝑓 = ω</em>0 + α𝑡$

• Period: $ω = (2π / 𝑇)$; $𝑇 = (2π / ω)$

• Frequency: $ω = 2π𝑓; 𝑓 = (ω / 2π)$

• Torque: $τ = 𝑟 × 𝐹 = 𝐹𝑟𝑠𝑖𝑛θ = 𝐹𝑟 ⊥$ (N·m).

• $τ = 𝐼α$

• Moment of Inertia: $𝐼 = \sum 𝑚 𝑖 𝑟 𝑖^2$ (kg m2).

  • Parallel Axis Theorem: $𝐼<em>{tot} = 𝐼</em>{orig} + 𝑚𝑟^2$

• Rotational Kinetic Energy: $𝐾𝐸 𝑟 = (1 / 2)𝐼ω^2$

• Angular Momentum:

  • $𝐿 = 𝑟 × 𝑝 = 𝑚𝑣𝑟 ⊥ = 𝑚𝑣𝑟𝑠𝑖𝑛θ$

  • $𝐿 = 𝐼ω$

• Angular Impulse: $\sum{τ} · 𝑡 = ∆𝐿 = 𝐼ω<em>f − 𝐼ω</em>0$

Lab Questions

• Start with "What do I want to know?"

• Based on the hypothesis.

• Relate to formula sheet.

• Multiple trials to reduce error.

Quantitative-Qualitative Translation

• Translate from algebra to English.

• Use math in the context of the question.

• Explain using physics logic.

Word Problems

1. A car travels a distance of 150 km in 2 hours. Calculate the speed of the car in km/h.

2. A runner completes a 200 m track in 25 seconds. Determine the velocity of the runner in m/s.

3. An object is dropped from a height of 45 m. Calculate the time it takes to reach the ground. Assume free fall.

4. A cyclist accelerates uniformly from rest to a speed of 20 m/s in 10 seconds. What is the acceleration of the cyclist in m/s²?

5. A ball is thrown vertically upward with an initial velocity of 15 m/s. Determine the maximum height it reaches before falling back down.

6. An object moving at a constant speed of 30 m/s travels a distance of 180 m. Calculate the time taken for this journey.

7. A plane descends with an acceleration of $g = -9.8 m/s²$. If it starts from rest, what will its velocity be after 5 seconds?

8. A diver jumps from a height of 10 m into the water below. How long does it take for the diver to reach the water's surface?

9. A vehicle is pushed forward with an applied force of 500 N, while experiencing a friction force of 200 N. What is the net force acting on the vehicle?

10. A satellite orbits the Earth at a radius of 7000 km. Calculate the centripetal force acting on the satellite, assuming the mass of the satellite is 1000 kg.

11. A spring has a spring constant of 250 N/m. If it is compressed by 0.1 m, find the force exerted by the spring.

12. An object in free fall drops from a height of 100 m. Calculate the work done on the object by gravity during its fall.

13. A 5 kg mass moves with a velocity of 10 m/s. What is the momentum of the mass?

14. An ice skater spins and doubles her angular velocity. Discuss how her angular momentum is affected by this change.

15. A pendulum has a period of 2 seconds. Calculate the frequency of oscillation in Hertz.

16. An object is dropped from a height, taking 3 seconds to reach the ground. Determine the height from which it was dropped.

17. An object moves at a uniform speed of 12 m/s for 30 seconds. Calculate the total distance traveled by the object in meters.

18. A box is pulled with a force of 600 N at an angle of 30° to the horizontal. What is the component of this force acting horizontally?

19. A car's engine does 600 J of work to accelerate to a speed of 20 m/s. Identify the type of energy change that occurs in the car.

20. An object is thrown vertically upwards with an initial speed of 25 m/s. Calculate the maximum height attained by the object before it begins to descend.

Answers

1. Speed = 75 km/h

2. Velocity = 8 m/s

3. Time = 3 seconds

4. Acceleration = 2 m/s²

5. Maximum height = 11.4 m

6. Time = 6 seconds

7. Velocity = -49 m/s

8. Time = 1.43 seconds

9. Net force = 300 N

10. Centripetal force = 14.29 N

11. Force = 25 N

12. Work = 980 J

13. Momentum = 50 kg m/s

14. Angular momentum increases (specifically doubles)

15. Frequency = 0.5 Hz

16. Height = 44.1 m

17. Distance = 360 m

18. Horizontal component = 519.62 N

19. Kinetic energy increase

20. Maximum height = 31.9 m