AP Physics 1

Chapter 1: Introduction, Measurement, Estimating

1. Uncertainty

   1. Uncertainty is assumed to be one or a few units in the last digit given

   2. Percent uncertainty can be determined with the numerical uncertainty/number

Chapter 2: Reference Frames and Displacement

1. Reference Frames and Displacement

   1. Reference frames are the scope of where something will be occurring

      1. For example u can see a person moving through a train seems to be moving at 85mph from outside the train while to someone on the train he is moving 5mph

   2. Position is where an object is in the x and/or y direction

      1. In general position is positive as an object moves to the right or upwards and is negative as an object move left or downward

   3. Displacement is how far on object is from its starting position

   4. Distance is how far in total an object has traveled

   5. A change in any value is equal to:

      1. Change in value = final value – initial value

   6. Vectors are quantities that have a direction and magnitude

2. Average Velocity

   1. Speed refers to how far an object travels within a given time period.

   2. Average Speed – the total distance traveled along its path divided by the time it takes the travel the distance

      1. Average speed = distance traveled/time elapsed

   3. Velocity is used to signify a direction as well as a magnitude or numerical value

   4. The average velocity is defined in terms of displacement instead of total distance

      1. Average velocity = displacement/time elapsed

   5. Elapsed time = change in time

3. Instantaneous Velocity

   1. Instantaneous Velocity – the average velocity over a short period of time

4. Acceleration

   1. When an object’s velocity is changing it is accelerating

   2. Average Acceleration – is the change in velocity divided by the time taken

      1. Average acceleration = change in velocity/time elapsed

   3. Acceleration is a vector quantity

   4. Instantaneous Acceleration – the average acceleration over a given instance of time, similar to instantaneous velocity

   5. Decelerating is when an object is slowing down, however it is not necessarily negative

   6. An object is decelerating when the velocity and acceleration are in opposite directions

5. Motion at Constant Acceleration

   1. You can use kinematics and other equations on the reference sheet to solve equations with constant acceleration

   2. Kinematics can only be used if acceleration is constant

   3. When an object has constant acceleration the instantaneous and average acceleration are the same

6. Solving Problems

   1. Do not think of physics as equations, but use its laws as well as equations in combination to solve problems

7. Freely Falling Objects

   1. The speed of a falling object is not proportional to its mass

   2. All objects will fall to earth with the same constant acceleration in the absence of air resistance

   3. Air resistance can affect light objects with a large surface area, however in most cases air resistance will be negligible 

   4. Acceleration due to gravity (g) is equal to 9.8 m/s^2

8. Graphical Analysis of Linear Motion

   1. The slope and area under the curve can help to get certain values

      1. For example in a distance vs. time graph the slope x/t can be found as the velocity

      2. Ex: Slope of the tangent line can be found as velocity in a distance vs. time graph

      3. Ex: The acceleration at any time is the slope of the tangent line in a velocity vs. time graph

Chapter 3: Kinematics in Two Dimensions; Vectors

1. Vectors and Scalars

   1. Vectors are quantities that have a magnitude and direction

   2. Scalar quantities only have a magnitude

2. Addition of Vectors

   1. In order to add or subtract vectors you need to get an x and y components for each and use Pythagorean theorem to solve for the resulting vector

3. Projectile Motion

   1. In projectile motion the process it took to get into this motion is neglected

   2. The x component for the objects velocity will stay constant if there is no air resistance present

   3. The only force acting upon an object in projectile motion is gravity meaning it is only accelerating downward

   4. Projectile motion is parabolic

Chapter 4: Dynamics: Newton’s Laws of Motion

1. Forces

   1. A force is needed to:

      1. Put an object in motion from rest

      2. To accelerate an object

      3. A force is a vector quantity with a direction and magnitude

   2. The typical unit for force is in Newtons (N)

2. Newton’s First law of Motion

   1. An object that is in motion stays in motion until acted upon by another force

   2. This is also called the law of inertia

3. Mass

   1. Mass is the measure of inertia of an object

   2. The typical SI unit for mass is kg

4. Newton’s Second Law of Motion

   1. F = ma

5. Newton’s Third Law of Motion

   1. For every action there is an opposite and equal reaction

6. Weight – The Force of Gravity and the Normal Force

   1. The force of gravity on an object is also known as that object’s weight

   2. The force of gravity is equal to F_g = mg

   3. The normal force is a contact force that acts perpendicular to the surface of contact

   4. Contact forces occur when objects are touching one another

Chapter 5: Circular Motion; Gravitation

1. Kinematics of Circular Motion

   1. Objects moving in a circle at a constant speed are in uniform circular motion

   2. Speed stays the same in circular motion, however velocity changes since its direction is constantly changing

   3. The centripetal acceleration points toward the center of the circular motion of an object

   4. Centripetal acceleration can be defined as: a_c = v²/r

2. Dynamics of Uniform Circular Motion

   1. When the velocity is constant in circular motion there will be a net force pointed toward the center if the circle

   2. Without a net force pointed to the center of the circle the object would move in a straight line

   3. The centripetal force is not a real force, but is the name given to another force like tension or gravity that puts the object in circular motion

   4. There is no outward force acting on an object in circular motion

3. Non-uniform Circular Motion

   1. If an object is not moving at a constant speed when it is moving in circular motion there is a force that is causing it to accelerate

   2. The force is tangent to the circle and will cause the net force to point at a certain angle rather than toward the center of the circle

4. Newton’s Law of Universal Gravitation

   1. Every particle in the universe attracts every particle with a force

      1. F_G = G(m₁m₂)/(r²)

      2. g = G(m1)/(r²)

5. Satellites and Weightlessness

   1. Satellites are kept in a relatively circular orbit due to their high speed around the earth

   2. Objects in orbit are technically in free fall however due to their high speeds they “miss” the earth

6. Kepler’s Laws

   1. Kepler’s first law states that the path of each planet around the sun is an ellipse with the sun at one focus of the ellipse 

   2. Kepler’s second law states that at certain points in  planets orbit it will move faster due to it being closer to the sun and slower due to it being farther from the sun. This creates sections of equal areas.

   3. Kepler’s third law states the period of any two planets is proportional to the distances.

      1. (T₁/T₂)² = (s₁/s₂)³           *s = the distance

Chapter 6: Work and Energy

1. Work Done by a Constant Force

   1. Work is defined as what is done when a force acts on an object

      1. W = F_||d or W = Fdcos(θ)

      2. SI unit: Joules(j) or N*m

2. Kinetic Energy and the Work Energy Principle

   1. Energy of motion is Kinetic Energy

      1. K = 0.5(m)(v)²

   2. The net work done on an object can be found as the objects change in kinetic energy

   3. Energy is in the same units as work Joules(j)

3. Potential Energy

   1. Potential Energy is the energy associated with forces that depend on the position or placement of an object

4. Conservative and Non-Conservative Forces

   1. Forces where the work done does not depend on the path of the object but its initial and final position are known as conservative forces

      1. EX: Gravity

   2. Forces where work depends on the path take are known as non-conservative forces

      1. EX: Friction

5. Mechanical Energy and Its Conservation

   1. When no conservative forces do any work on an object the change in potential and kinetic energy is zero. The sum of the initial and final kinetic and potential energy is the same.

   2. Energy is conserved so the total mechanical energy remains the same

   3. The total energy in any process neither decreases or increases, but can be transformed from one form to another

6. Power

   1. Power is the rate at which work is done

      1. P = work/time = change in energy/time

   2. Power has the SI unit of watt(W) or J/s

Chapter 7: Linear Momentum

1. Momentum

   1. Momentum can be defined as:

      1. p = mv

   2. Momentum is a vector quantity

   3. Impulse is equal to:

      1. Change in momentum = Ft

2. Conservation of Momentum

   1. Momentum is conserved in a system so the initial momentum and final momentum of a system will be constant as long as there is no external forces applied to the system

3. Elastic Collisions

   1. In an elastic collision the total kinetic energy is conserved

4. Inelastic Collisions

   1. In an inelastic collision the total kinetic energy is not conserved

      1. This is due to heat or another form of energy

   2. If two objects stick together this is known as a completely inelastic collision

5. Center of Mass

   1. The center of mass is one point that moves in a path that a particle would take if the net force of the system were to be applied to it

   2. The center of mass could be for one object or a bunch of different objects moving in different directions

   3. The position of the center of mass can be found with:

      1. x = m_ax_a + m_bx_b +…. /the sum of all the masses

Chapter 8: Rotational Motion

1. Angular Quantities

   1. Angular position is equal to the angle θ of a line

   2. For calculations in rotational motion angles are measured in radians

      1. Make sure the calculator is in radians when calculating any angular motion

      2.  Θ = l/r

   3. Angular velocity: ω = θ/t

   4. Angular velocity has units of radians/sec

   5. All points in a rigid object will rotate with the same angular velocity

   6. Angular Acceleration: α = ω/t

   7. The normal values of any angular value can be found by multiplying the value by r

      1. EX: a = αr, v = ωr

   8. I is equal to inertia and its value differs between objects

      1. The equation for inertia of an object should be given

2. Rolling Motion 

   1. In order for an object to rotate a frictional force needs to be applied

   2. If there is not friction rather than rolling an object would just slide across the surface

   3. When rolling an object has both rotational and translational motion

3. Torque

   1. The torque or an object can be found with:

      1. τ = F_{perpendicular} * r or Frsinθ

      2. τ = Iα *similar to F=ma

   2. The torque relies on the magnitude of the force as well as the distance that force is being applied from the axis

   3. If there are multiple torques the angular acceleration is proportional to the net torque

4. Rotational Kinetic Energy

   1. An object rotating around an axis has rotational kinetic energy

   2. Rotational Kinetic Energy can be defined as:

      1. K = 0.5(I)(ω)²

   3. When calculating energy equations with rotational energy you do not need to include static friction as static friction is the rotational energy since friction causes the rotation

   4. Work that is done by torque can be calculated as:

      1. W = τ Δθ

   5. Power can be defined as:

      1. P = W/t = (τ Δθ)/t = τω

5. Angular Momentum

   1. Angular Momentum is:

      1. L = Iω

   2. The net torque can be found using angular momentum:

      1.  Στ = τ_net = ΔL/Δt

   3. Angular momentum is a conserved quantity like normal momentum

   4. The total angular momentum or a rotating object remains constant as long as the net torque acting on the object is zero

Chapter 11: Oscillations and Waves

1. Simple Harmonic Motion

   1. The equilibrium position is where there is no force exerted or the force is equal to zero

      1. Often the equilibrium is x = 0

   2. At the equilibrium position the velocity is at its maximum

      1. This means kinetic energy will also be at a maximum at this point

   3. At a position of x = A the object will stop and the potential energy will be at a maximum

   4. In simple harmonic motion the object will continue to go between x = A and  x = -A 

   5. Period is the time required to complete one cycle

   6. Frequency is the number or complete cycles per second

   7. Frequency and Period are inversely related

      1. T = 1/f

   8. Simple harmonic motion will only occur if friction is negligible within the system so the total mechanical energy can stay constant

   9. The maximum displacement is known as the amplitude

   10. The position on SHM can be found as:

       1. x = Acos(2π f t) 

   11. Velocity can be found as:

       1. v = -v_max sin(2π f t)

   12. Acceleration can be found as:

       1. a = -a_max cos(2π f t) 

2. Resonance

   1. Resonance is also known as the fundamental frequency or f₀

      1. The equations for period on the reference table can be converted to find fundamental frequency

3. Wave Motion

   1. Waves that occur in matter are known as mechanical waves

   2. Amplitude is the maximum height of a crest or the lowest point for a trough compared to the equilibrium level

   3. Wavelength is the distance between two successive crests or troughs

   4. Frequency is the number or crest or complete cycles for a wave

   5. Period is the time between two successive crests

4. Transverse and Longitudinal Waves

   1. Transverse waves are when the particles move back and forth perpendicular to the direction the wave is going

   2. Longitudinal waves are when the particles are moving back and forth parallel to the direction of the wave

   3. The speed of a transverse wave can be found with:

      1. v = √F_T/μ

5. Reflection

   1. When a wave is reflected its amplitude is reversed and its direction is changed

6. Interference

   1. Interference is when two waves pass through one another

   2. Often the waves will combine to form a larger wave or smaller wave

   3. Destructive interference is when the two waves combine and have zero amplitude

   4. Constructive interference is when the waves combine to form a larger amplitude

7. Refraction

   1. Refraction is when a wave crosses into another medium and can be changed to move in another direction

      1. EX: Pencil in water

8. Diffraction

   1. Diffraction is when waves bend around an object

1. Acceleration
   a = \frac{\Delta v}{\Delta t}

2. Kinematic Equations for Uniformly Accelerated Motion

   1. vf = vi + at

   2. d = v_i t + \frac{1}{2}at^2

   3. vf^2 = vi^2 + 2ad

3. Work
   W = Fd \cos(\theta)

4. Kinetic Energy
   KE = \frac{1}{2}mv^2

5. Potential Energy (Gravitational)
   PE = mgh

6. Power
   P = \frac{W}{t} = Fv \cos(\theta)

7. Momentum
   p = mv

8. Impulse
   J = F \Delta t = \Delta p

9. Hooke's Law
   F_{spring} = -kx

10. Period of a Simple Pendulum
    T = 2\pi \sqrt{\frac{L}{g}}

11. Frequency of a Simple Harmonic Oscillator
    f = \frac{1}{T}

12. Elastic Collision (in one dimension)

    • Conservation of Momentum:
      m1v{1i} + m2v{2i} = m1v{1f} + m2v{2f}

    • Conservation of Kinetic Energy:
      KE{initial} = KE{final}

13. Inelastic Collision
    m1v{1i} + m2v{2i} = (m1 + m2)v_f

14. Torque
    \tau = rF \sin(\theta)

15. Rotational Kinetic Energy
    KE_{rot} = \frac{1}{2} I \omega^2

16. Angular Momentum
    L = I\omega

17. Mass-energy equivalence
    E = mc^2

18. Gravitational Force
    F_g = \frac{GMm}{r^2}

    • Where G is the gravitational constant, G = 6.67 × 10^{-11} N(m/kg)^2

19. Center of Mass
    x{cm} = \frac{mx1 + mx2}{m1 + m_2}

20. Wave Speed
    v = f \lambda

Each equation here is essential for understanding core concepts in AP Physics 1 and may appear in problems not

1. Acceleration
   a = \frac{\Delta v}{\Delta t}

2. Kinematic Equations for Uniformly Accelerated Motion

   1. vf = vi + at

   2. d = v_i t + \frac{1}{2}at^2

   3. vf^2 = vi^2 + 2ad

3. Work
   W = Fd \cos(\theta)

4. Kinetic Energy
   KE = \frac{1}{2}mv^2

5. Potential Energy (Gravitational)
   PE = mgh

6. Power
   P = \frac{W}{t} = Fv \cos(\theta)

7. Momentum
   p = mv

8. Impulse
   J = F \Delta t = \Delta p

9. Hooke's Law
   F_{spring} = -kx

10. Period of a Simple Pendulum
    T = 2\pi \sqrt{\frac{L}{g}}

11. Frequency of a Simple Harmonic Oscillator
    f = \frac{1}{T}

12. Elastic Collision (in one dimension)

    • Conservation of Momentum:
      m1v{1i} + m2v{2i} = m1v{1f} + m2v{2f}

    • Conservation of Kinetic Energy:
      KE{initial} = KE{final}

13. Inelastic Collision
    m1v{1i} + m2v{2i} = (m1 + m2)v_f

14. Torque
    \tau = rF \sin(\theta)

15. Rotational Kinetic Energy
    KE_{rot} = \frac{1}{2} I \omega^2

16. Angular Momentum
    L = I\omega

17. Mass-energy equivalence
    E = mc^2

18. Gravitational Force
    F_g = \frac{GMm}{r^2}

    • Where G is the gravitational constant, G = 6.67 × 10^{-11} N(m/kg)^2

19. Center of Mass
    x{cm} = \frac{mx1 + mx2}{m1 + m_2}

20. Wave Speed
    v = f \lambda

Each equation here is essential for understanding core concepts in AP Physics 1 and may appear in problems not

1. Understand the Concepts

   • Make sure you have a clear understanding of the physical principles and concepts behind the equation you are trying to derive.

2. Identify Known Quantities

   • List all the quantities given in the problem and their relationships. Write down any values (variables) you might need to use.

3. Write Down Relevant Equations

   • Gather the equations related to the concepts you are working with, including definitions and any known relationships. Identify which ones are foundational and can be manipulated.

4. Choose a Target Equation

   • Decide the equation you want to derive based on the known quantities and concepts.

5. Rearrange Known Equations

   • Take the relevant equations and algebraically manipulate them to solve for the unknown quantities. Make sure to clearly state each manipulation step.

6. Substitute Values

   • Replace the known quantities into the newly derived equation. Ensure units are consistent and properly converted where necessary.

7. Check Dimensions

   • When deriving, make sure your final equation dimensions are consistent with what they should be. For example, speed should have units of distance/time.

8. Validate Your Result

   • Once you have the final equation, think logically about whether it makes sense physically and if it corresponds to known scenarios or limits.

9. Practice

   • Regularly practice different derivations to build familiarity. Use various problems to apply different concepts.