AP Physics 1 Review

Linear

Linear

y is proportional to x

Quadratic

y is proportional to x²

Inverse

y is proportional to 1/x

Square-Root

y is proportional to √x

Proportional Reasoning

Graphs and equations are useful because they tell us how two variables are related. You should be able to take a change in one variable and describe how it changes another variable.

Linearization and Graph Analysis

To analyze a graph, an equation can be matched to y = mx + b

• Y-Axis Variable (y): Variable by itself

• X-Axis Variable (x): On the opposite side of the y-variable but has a direct connection to it

• Slope (m): If the x-axis variable has a constant to it, that number becomes the slope

It is important in linearization to correctly modify the slope of the new equation so that it is adjusted to a linear form

Motion in One Direction

AP formula sheet uses x(final position) and x₀(initial position)

Motion at Constant Velocity

Equations:

• ∆x = vt

• x = vt + x₀

Graphs and Proportions: Linear

CANNOT be used when there is acceleration!

Motion with Acceleration

Kinematic Equations:

• x = x₀ + v₀t + 1/2at²

• v = v₀ + at

• v² = v₀² + 2a(x - x₀)

DO NOT use if the acceleration is not constant!

What do Slope and Area Under the Curve Represent on a Position versus Time Graph?

Slope: Velocity

Area Under the Curve: N/A

What do Slope and Area Under the Curve Represent on a Velocity versus Time Graph?

Slope: Acceleration

Area Under the Curve: Displacement (change in position)

What do Slope and Area Under the Curve Represent on a Acceleration versus Time Graph?

Slope: Jerk (the rate of change of an object’s acceleration over time)

Area Under the Curve: Change in velocity

Free Fall

Motion where the acceleration is 9.8 m/s² downwards

The speed of a vertical projectile is zero at its maximum height

Motion in Two Dimensions

Horizontal and vertical motions happen simultaneously but independently (their information is not shared between the two)

• Exception: Time

Projectile Motion is a type of two-dimensional motion

• Horizontal speed is constant

• Vertical motion has a downward acceleration of 9.8 m/s²

• Maximum range occurs at 45° launch angle

• The projectile should return to the ground with the same speed (on level ground)

• Vertical speed = zero at maximum height (NOT TRUE FOR HORIZONTAL SPEED)

Newton’s First Law

The motion of an object only changes when there is a net (unbalanced) force

• Objects at rest or moving at constant speed have balanced forces

• Objects that are changing speed or direction (accelerating) DO have a net force

An object at rest remains at rest unless acted upon by an outside force

Newton’s First Law

Newton’s Second Law

Describes the acceleration that results when a net force is applied to an object

Solving this equation for mass gives the inertial mass

Equations:

• a = F_net/m

• F_net = ma

Force equals an object’s mass times its acceleration

Newton’s Second Law

Newton’s Third Law

Objects interact with each other by exerting equal forces on each other in opposite directions

• If you exert a force on an object, that object MUST exert the same force back on you

• Although the force pairs MUST be equal, the forces can have different effects based on the different masses of the objects

Every action has an equal and opposition reaction

Newton’s Third Law

Forces

Horizontal and vertical forces must be accounted for separately

Measured in newtons (N)

Constant Forces

Examples:

• Force of Gravity/Weight (F_g)

• Normal Force (F_N)

• Tension Force (F_T)

• Friction Force (F_f)

Force of Gravity/Weight (F_g)

The attraction between two objects with mass

Equations:

• F_g = mg

• F_g = GMm/r²

Solving for m gives the gravitational mass

Normal Force (F_N)

A support force perpendicular to the surface

Often helps to counteract with a downward pull of gravity (NOT ALWAYS THE CASE)

Tension Force (F_T)

Force in a string/spring/stretchable object that points toward the center of that object

Friction Force (F_f)

A force between two surfaces

• Slow objects down

• Prevent objects from fully speeding up

• Keep objects at rest relative to each other

Non-Constant Forces

Examples:

• Drag Force/Air Resistance

• Spring Force (k)

Drag Force/Air Resistance

A speed-dependent force that slows down objects moving in a fluid, such as air

Spring Force

A displacement-dependent force that tried to restore a spring to its equilibrium position

Centripetal Force (F_c)

A center-pointing force that is the reason objects move in circular paths (change the direction of motion, but not the speed)

Equation (measured in newtons)

NOT a new type of force → a name given to other forces when they cause objects to move in a circular path

Uniform Circular Motion

Occurs when objects rotate with constant speed

Velocity is always changing because of direction change

Has centripetal acceleration but not tangential acceleration

Non-Uniform Rotation

Occurs when the rotational speed is changing

Motion is described with rotational versions of kinematic and dynamics

Fundamentals and Newton’s Laws still apply → most importantly rotational acceleration can only occur with net torque occurring on an object

α = τ_NET/I is Newton’s Second Law for Rotation and is the basis of any rotational dynamics problem

Rolling Motion

Occurs when an object moves both translationally (linearly) and rotates at the same time (both must be accounted for)

Planetary Motion

The orbits of planets are elliptical but can be approximated to circular

Gravity (F_g = GMm/r²) provides the centripetal force

Orbital Velocity (v = √GM/r) which can be derived by setting F_g = F_{NET C}

g can be called acceleration due to gravity (m/s²) OR gravitational field strength (N/kg)

System

The group of objects for which a person is tracking the energy or momentum

• Should always be defined for conserved qualities (ex. energy, momentum, and angular momentum)

Internal Force: A force exerted between one object in the system on another object in the system

External Force: A force exerted from an object outside of the system onto an object inside the system

Closed Systems

NO external forces present

Energy/momentum/angular momentum are CONSERVED

Open Systems

External forces present

Energy/momentum/angular momentum are NOT CONSERVED

Conservation of Energy

In every system, energy must be conserved or accounted for

• If a system gains energy, it must be through the action of an external force, and another system must lose the same amount of energy

Energy Conservation statement/starting point: E_i ± W_ext = E_f

Kinetic Energy

The energy of motion

Measured in Joules (J)

Equations:

• Translation: 1/2mv²

• Rotation: 1/2Iω²

Potential Energy

The energy based on position

Measured in Joules (J)

Equations:

• Gravitational PE: U_g = mgh

  • Based on height

• Elastic/Spring PE: U_s = 1/2k∆x²

  • Based on stretch/compression distance

Work

The change in kinetic energy

Measured in Joules (J)

Equation:

• W = Fd * cosθ

The area under a F vs d graph

Conservation of Momentum

In every system, momentum and angular momentum must be conserved and accounted for

• If a system gains momentum, it must be through the action of an external force, and another system must lose the same amount of momentum

Linear Momentum

Measured in kg * m/s

Equation:

• Translational Motion: p = mv

Angular Momentum

Measured in kg * m²/s

Equations:

• Rotational Motion: L = Iω

• A point mass: L = rmv

Impulse

The change in momentum

Measured in N * s

Equation:

• J = ∆p = F∆t

Impulse is the area under a F vs t graph

Angular Impulse

The change in angular momentum

Measured in kg * m²/s

Equation:

• ∆L = τ_NET * ∆t

Rules of Momentum in Collisions

Newton’s Third Law states the forces on each body must be equal and opposite

Impulse and change in momentum are therefore also equal and opposite (whatever momentum one object gains, the other loses)

The momentum of the system is CONSERVED

Rules of Elasticity in Collisions

Depends on how much kinetic energy is conserved

• Perfectly Elastic: All KE is conserved, and objects bounce off each other without deforming

• General Inelastic: Some KE is lost, and objects bounce off each other

• Perfectly Inelastic: Maximum possible KE is lost (NOT all), and objects stick together

Momentum and energy in total should be CONSERVED in all collisions with appropriate systems

Conservation of Angular Momentum

Used when a translating object interacts with a rotating one

• Ex. Throwing a ball from a merry-go-round or a bat hitting a baseball

Used for a single rotating object changing shape

• Ex. A figure skater pulls in her arms → momentum of inertia decreases so angular velocity must increase to keep angular momentum constant

Center of Mass

A point that can be used to represent an entire object

• Objects are balanced if the center of mass is supported

• The velocity of the center of mass does not change in a collision where linear momentum is conserved

Oscillating Motion

Caused by a force that is

• Proportional to displacement

• Acts to restore the object to its equilibrium position

Period (T)

Used to measure time for one oscillation

Frequency (f)

Measures the number of oscillations in one second

Angular frequency (ω)

Measures the number of oscillations in 2π seconds

Trigonometric Functions

Used to describe position, velocity, and acceleration

Equations:

• Usually:

  • These are valid when the clock starts at the amplitude, otherwise the graph is shifted horizontally:

    • Position: x α cos(t)

    • Velocity: v α - sin(t)

    • Acceleration: a α - cos(t)

• Position-Time Function for an Oscillator: x(t) = Acos(ωt) = Acos(2πf * t)

When Position is at a Maximum Magnitude

Velocity is zero

Acceleration is a maximum magnitude

Position and acceleration have opposite signs

When Displacement is Zero

Velocity is a maximum magnitude

Acceleration is zero

What does Changing the Amplitude of Oscillation do?

It affects the energy but NOT the timing of the oscillation

Conservation of Energy

A good strategy to use in oscillation problems when comparing two points

When Should Energy be used in a Problem?

If….

• There's a height change involved

• There's a spring involved

• A force acts over a given distance

When Should Momentum be used in a Problem?

If…

• Multiple objects are interacting with each other

• There is a collision

• A force acts over a time interval

When Should Dynamics and Kinematics be used?

If…

• Energy and momentum don't work

• You need to explain WHY motion occurs

What Framework Should you use in Paragraph-Length Responses and Justifying Answes?

Claim-Evidence-Reasoning Framework

Problem-Solving Task Verbs

Pay special attention to the verb used in the questions

Different task verbs require different types of answers

Ex. Calculate, compare, determine, evaluate, explain, justify, label, plot, sketch/draw, state/indicate/circle, verify

Calculate

Perform mathematical steps to arrive at a final answer, including algebraic expressions, properly substituted numbers, and correct labeling of units and significant figures

Phrased as “What is?”

Compare

Provide a description or explanation of similarities and/or differences

Derive: Perform a series of mathematical steps using equations laws to arrive at a final answer

Describe: Provide the relevant characteristics of a specified topic

Determine

Make a decision or arrive at a conclusion after reasoning, observation, or applying mathematical routines (calculations)

Evaluate

Roughly calculate numerical quantities, values (greater than, equal to, or less than), or signs (negative or positive) of quantities based on experimental evidence of provided data

When making estimations, showing steps in calculations is not required

Explain

Provide information about how or why a relationship, process, pattern, position, situation, or outcome occurs by using evidence and/or reasoning to support or qualify a claim

Explain “how”: Typically requires analyzing the relationship, process, pattern, position, situation, or outcome

Explain “why”: Typically requires analysis of motivations or reasons for the relationship, process, pattern, position, situation, or outcome

Justify

Provides evidence to support, qualify, or defend a claim, and/or provide reasoning to explain how that evidence supports or qualifies the claim

Label

Provides labels indicating unit, scale, and/or components in a diagram, graph, model, or representation

Plot

Draw data points in a graph using a given scale or indicating the scale and units, demonstrating consistency between different types of representations

Sketch/Draw

Create a diagram, graph, representations, or model that illustrates or explains relationships or phenomena, demonstrating consistency between different types of representations

Labels may or may not be required

State/Indicate/Circle

Indicate or provide information about a specific topic, without elaboration or explanation

Also phrased as “What…?” or “Would…?” interrogatory questions

Verify

Confirm that the conditions of a specific definition, law, theorem, or test are met in order to explain why it applies in a given situation

Use empirical data, observations, tests, or experiments to prove, confirm, and/or justify a hypothesis