AP Physics 1 Exam

Displacement (Δx)

-Net change in position

-Measured in meters (m)

Δx = x(f) - x(i)

Velocity (v)

-Speed and direction

-Measured in meters per second (m/s)

average v = Δx/t

Acceleration (a)

-Rate of change of velocity w/ respect to time

-Measured in meters per second squared (m/s^2)

average a = Δv/t

Speeding up vs. Slowing Down

-Speeding up occurs when velocity and acceleration have the same sign

-Slowing down occurs when velocity and acceleration have opposite signs

Position vs. Time Graph

-Slope represents average velocity

-Object changes direction when graph crosses x-axis

Velocity vs. Time Graph

-Slope represents average acceleration

-Area represents displacement

Acceleration vs. Time Graph

-Area represents change in velocity

Scalars

Quantities with only a size/magnitude (ex: speed, mass, length, temperature, time, distance, energy, etc.)

Vectors

Quantities with both a size and direction (ex: displacement, velocity, position, acceleration, force, etc.)

Projectile Motion

-Horizontal and vertical components are independent of each other

-Complementary angles travel same horizontal distance

-Larger angles travel higher and spend more time in air, while smaller angles have greater horizontal velocities

Force (F)

-A push or pull

-Measured in Newtons (N)

Newton's 1st Law

An object will move at a constant velocity in a frictionless, airless vacuum unless another force is exerted on it

Inertia

-property of an object that resists a change in motion

-measured in mass

Newton's 2nd Law

Net force = mass x acceleration

Newton's 3rd Law

Every action has an equal and opposite reaction

Normal Force (Fn)

A contact force between force between two hard surfaces

Weight

-Force of gravity on an object

-Depends on mass of object and strength of gravitational field

-Measured in Newtons (N)

Mass

-How much stuff an object is made of

-Mass is independent of location of object

-Measured in kilograms (kg)

Static Friction (Fs)

Force that resists motion of two objects that are stationary relative to one another

Fs (max) = Us x Fn

Kinetic Friction (Fk)

Friction when two objects slide against each other

Fk = Uk x Fn

Hooke's Law

Fs = kΔx, where k is the spring constant

Momentum (p)

p = mv

-Measured in kg x m/s

-momentum is conserved in collisions and explosions

Impulse (J)

J = Fnet Δt = Δp

-Measured in N x s

Elastic Collisions

-Momentum and kinetic energy are conserved

-Can use equation v1(i) - v2(i) = v2(f) - v1(f)

Inelastic Collisions

-Momentum is conserved BUT kinetic energy is not conserved

-Collision is completely inelastic if objects stick together

Translational Kinetic Energy (K)

-Energy of objects in motion

-Measured in joules

K = 1/2 mv^2

Gravitational Potential Energy (Ug)

-Energy of an object based on its position

-Measured in joules

Ug = mgh

Elastic Potential Energy (Ue)

-Energy of a spring

-Measured in joules

Ue = 1/2 kx^2

Work (W)

W = FΔxcosϴ

W = ΔK

Power (P)

The amount of work done over time, measured in Watts (W)

P = W/t

Conservative Forces

-The amount of work done by the force does not depend on its path

-Mechanical energy is conserved

Nonconservative Forces

-The amount of work done by the force depends on its path

-Mechanical energy is not conserved

Centripetal Acceleration

-Acceleration towards the center of a circle

Ac = v^2 / r

Conditions for Circular Motion

1. Net force must point toward center of circle

2. Velocity must point tangent to circle

Period (T)

Time to complete one cycle or revolution

T = 2∏r/v

Frequency (f)

Number of cycles per second

f = 1/T, measured in Hertz (Hz)

Centripetal Force

The net force (not a real force) that points toward the center of a circle

Fictitious Force

-A fake force that appears in an accelerating reference frame

-Can be explained by looking at the situation from a non-accelerating reference frame

Newton's Universal Law of Gravitation

Fg = Gm1m2/r^2, where G is the universal gravitational constant

Gravitational Fields

-Any object with mass creates a gravitational field around itself that expands infinitely in all directions

-The field exerts a gravitational force on any other object with mass

Gravitational Field Strength

-Gravitational field strength varies depending on location

g = Gm2/r^2

Gravitational Potential Energy in Outer Space

Ug = -Gm1m2/r, where r is the distance between the objects

-Zero position is defined as infinitely far away

Orbiting

-To orbit, an object must have an initial velocity tangent to the Earth

-Gravity provides the centripetal acceleration

Circular vs. Elliptical Orbits

Circular Orbits: radius is constant, Ug is constant, and K is constant

Elliptical Orbits: radius is NOT constant, Ug is greater farther away, and K is greater closer to planet

Restoring Force

-Force pointing toward equilibrium position

Restoring force = kΔx, where k is the restoring constant

Simple Harmonic Motion

A repeated, back and forth motion that is caused by a restoring force

Period of SHM

The amount of time required to complete once cycle of motion

T spring = 2∏√(m/k)

T pendulum = 2∏√(L/g)

Angular Frequency (w)

Frequency measured in radians per second (rads/s)

w = 2∏f = 2∏/T

Amplitude (A)

The maximum displacement from equilibrium

Displacement in SHM

-Displacement is zero at equilibrium and maximum at extreme positions

x(t) = Acost(wt + ϴ), where ϴ is the phase constant/shift

Velocity in SHM

-Velocity is the 1st derivative of displacement

-Maximum velocity occurs at equilibrium

Acceleration in SHM

-Acceleration is the 2nd derivative of displacement

-Maximum acceleration occurs at extreme positions

Transverse Waves

Particles vibrate perpendicular to direction of wave (ex: wave on rope)

Longitudinal Waves

Particles vibrate parallel to direction of wave (ex: sound waves)

Wavespeed

-Wave speed depends on physical properties of the medium (NOT frequency or wavelength)

v = ƛf

Superposition

Two waves run into each other → constructive interference (adding amplitude) or destructive interference (subtracting amplitude)

Beats

When sound waves with slightly different frequencies meet, the interference is alternately constructive and destructive, so the sound gets louder and softer at regular intervals

Standing Waves

-Created when two waves of equal amplitude and equal frequency interfere continuously

-Can have two fixed ends, two open ends, or one open and one closed end

Dopple Effect

-When a source moves towards an observer, the wavelength decreases and the frequency increases

-When an observer moves towards a source, the wavelength stays the same but the frequency increases

Resonance

Objects have a natural (resonant) frequency it liked to oscillate at

Rotational Position

-Position defined by angle ϴ

-Measured in radians

Angular Velocity (w)

-Change in angle over time

-Measured in radians per second (rads/s) or revolutions per minute (rpm)

w = Δϴ/t

Angular Acceleration (α)

-Change in angular velocity over time

-Measured in radians per second squared (rads/s^2)

α = Δw/t

Angular Kinematics

Δϴ = 1/2 αt^2 + w(o)t + x(o)

w(f)^2 - w(i)^2 = 2αΔϴ

Torque (T)

-Torque depends on amount of applied force, distance from pivot point, & angle between force and distance

T = Frsinϴ

Tnet = Iα

Rotational Inertia (I)

Inertia that resists rotation/twisting

I = mr^2 for a point mass

Angular Momentum (L)

L = Iw, measured in kg x m^2/s^2

Angular momentum is conserved if no net torque is applied

Rotational Kinetic Energy (Krot)

Krot = 1/2 Iw^2

Coulomb's Law

F = k|q1||q2|/r^2, where k is the Coulomb's law constant

Conductors vs. Insulator

Conductors: objects/materials in which charge can flow freely

Insulators: objects that restrict the flow of charge

Voltage (V)

-The electric potential energy per coulomb

-Measured in Volts (V)

Current (I)

-The rate of flow of charge

-Measured in amperes (A)

-Current flows in the direction positive charges would move

Resistance (R)

-A measure of how difficult it is for electrons to moved through a material

-Measured in Ohms (Ω)

-Resistance increases with resistivity (density) and length BUT decreases with area

Ohm's Law

-The resistance in an ohmic device is constant, independent of current and voltage

V = IR

Parallel Circuit

-There are multiple paths through the circuit

-Resistors share total current

-Electrons use up all of their voltage at one resistor

Series Circuit

-There is only one path through the circuit

-Resistor each draw total current

-Electrons split their electrical energy between each resistor

Power in a Circuit (P)

-Change in electrical energy over time

P = IΔV

Energy Efficiency

Ratio of useful output energy over total input energy

Light bulbs

-Brightness depends on power

-Bulbs with less watts shine brighter in series b/c they have greater resistance

-Bulbs with less watts shine less in parallel b/c they have less resistance