Margins Study Assistant

Chapter 1

Units and Measurement

Summary

Two commonly used systems of units are English units and SI units. Physics is about trying to find the simple laws that describe all natural phenomena Scientists attempt to describe the world by formulating models, theories, and laws Systems of units are built up from a small number of base units, which are defined by accurate and precise measurements of conventionally chosen base quantities.

Key terms

units: standards used for expressing and comparing measurements
base unit: standard for expressing the measurement of a base quantity within a particular system of units; defined by a particular procedure used to measure the corresponding base quantity
law: description, using concise language or a mathematical formula, of a generalized pattern in nature supported by scientific evidence and repeated experiments
physics: science concerned with describing the interactions of energy, matter, space, and time; especially interested in what fundamental mechanisms underlie every phenomenon
SI units: the international system of units that scientists in most countries have agreed to use; includes units such as meters, liters, and grams
English units: system of measurement used in the United States; includes units of measure such as feet, gallons, and pounds
model: representation of something often too difficult (or impossible) to display directly
order of magnitude: the size of a quantity as it relates to a power of 10

Chapter 2

Vectors

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Summary

A vector quantity is any quantity that has magnitude and direction, such as displacement or velocity. The length of the vector is its magnitude, which is a positive scalar. The direction angle of a vector is a scalar Parallel vectors have the same direction angles but may have different magnitudes.

Key terms

vector: mathematical object with magnitude and direction
vector quantity: physical quantity described by a mathematical vector—that is, by specifying both its magnitude and its direction; synonymous with a vector in physics
length of the vector: its magnitude, which is a positive scalar
direction angle: in a plane, an angle between the positive direction of the x -axis and the vector, measured counterclockwise from the axis to the vector
direction of a vector: given by the angle the vector makes with a reference direction, often an angle with the horizontal
scalar: a number, synonymous with a scalar quantity in physics
parallel vectors: two vectors with exactly the same direction angles

Chapter 3

Motion Along a Straight Line

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Summary

Displacement is the change in position of an object. Distance traveled is the total length of the path traveled between two positions Kinematics is the description of motion without considering its causes. The SI unit for displacement is the meter.

Key terms

kinematics: the description of motion through properties such as position, time, velocity, and acceleration
distance traveled: the total length of the path traveled between two positions
position: the location of an object at a particular time
displacement: the change in position of an object
two-body pursuit problem: a kinematics problem in which the unknowns are calculated by solving the kinematic equations simultaneously for two moving objects
average velocity: the displacement divided by the time over which displacement occurs under constant acceleration
average acceleration: the rate of change in velocity; the change in velocity over time
free fall: the state of movement that results from gravitational force only

Chapter 4

Motion in Two and Three Dimensions

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Summary

The displacement vector Δ r → gives the shortest distance between any two points on the trajectory of a particle in two or three dimensions The velocity vector is tangent to the trajectory of the particle Graphically, it is a vector from the origin of a chosen coordinate system to the point where the particle is located at a specific time Instantaneous velocity gives the speed and direction of a particle at a specific time on its trajectory in two or three dimensions, and is a vector in two and three dimensions

Key terms

velocity vector: vector that gives the instantaneous speed and direction of a particle; tangent to the trajectory
displacement vector: vector from the initial position to a final position on a trajectory of a particle
trajectory: path of a projectile through the air
point where the particle: located at a specific time
centripetal acceleration: component of acceleration of an object moving in a circle that is directed radially inward toward the center of the circle
reference frame: coordinate system in which the position, velocity, and acceleration of an object at rest or moving is measured
tangential acceleration: magnitude of which is the time rate of change of speed. Its direction is tangent to the circle
angular frequency: ω , rate of change of an angle with which an object that is moving on a circular path

Chapter 5

Newton's Laws of Motion

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Summary

A free-body diagram is a drawing of all external forces acting on a body Dynamics is the study of how forces affect the motion of objects, whereas kinematics simply describes the way objects move External forces are any outside forces that act on a body.

Key terms

newton: SI unit of force; 1 N is the force needed to accelerate an object with a mass of 1 kg at a rate of 1 m/s 2
free-body diagram: sketch showing all external forces acting on an object or system; the system is represented by a single isolated point, and the forces are represented by vectors extending…
force: push or pull on an object with a specific magnitude and direction; can be represented by vectors or expressed as a multiple of a standard force
external force: force acting on an object or system that originates outside of the object or system
dynamics: study of how forces affect the motion of objects and systems
inertia: ability of an object to resist changes in its motion
law of inertia: see Newton’s first law of motion

Chapter 6

Applications of Newton's Laws

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Summary

The normal force on an object is not always equal in magnitude to the weight of the object. Some problems contain multiple force vectors acting in different directions on an object. Always analyze the direction in which an object accelerates so that you can determine whether F net = m a or F net = 0 If an object is accelerating vertically, the normal force is less than or greater than the weight of the object.

Key terms

object: accelerating vertically, the normal force is less than or greater than the weight of the object
drag force: force that always opposes the motion of an object in a fluid; unlike simple friction, the drag force is proportional to some function of the velocity of the object in that fluid
terminal velocity: constant velocity achieved by a falling object, which occurs when the weight of the object is balanced by the upward drag force
static friction: force that opposes the motion of two systems that are in contact and are not moving relative to each other
kinetic friction: force that opposes the motion of two systems that are in contact and moving relative to each other
banked curve: curve in a road that is sloping in a manner that helps a vehicle negotiate the curve
ideal banking: sloping of a curve in a road, where the angle of the slope allows the vehicle to negotiate the curve at a certain speed without the aid of friction between the tires and the…

Chapter 7

Work and Kinetic Energy

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Summary

The work done against a force is the negative of the work done by the force The kinetic energy of a particle is the product of one-half its mass and the square of its speed, for non-relativistic speeds The kinetic energy of a system is the sum of the kinetic energies of all the particles in the system The infinitesimal increment of work done by a force, acting over an infinitesimal displacement, is the dot product of the force and the displacement

Key terms

work: done when a force acts on something that undergoes a displacement from one position to another
kinetic energy: energy of motion, one-half an object’s mass times the square of its speed
kinetic energy of a particle: the product of one-half its mass and the square of its speed, for non-relativistic speeds
kinetic energy of a system: the sum of the kinetic energies of all the particles in the system
work done against a force: the negative of the work done by the force
work-energy theorem: net work done on a particle is equal to the change in its kinetic energy
average power: work done in a time interval divided by the time interval
net work: work done by all the forces acting on an object

Chapter 8

Potential Energy and Conservation of Energy

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Summary

For a conservative force, the infinitesimal work is an exact differential. A non-conservative force is one for which the work done depends on the path For a single-particle system, the difference of potential energy is the opposite of the work done by the forces acting on the particle as it moves from one position to another The potential energies for Earth’s constant gravity, near its surface, and for a Hooke’s law force are linear and quadratic functions of position, respectively

Key terms

potential energy: function of position, energy possessed by an object relative to the system considered
exact differential: is the total differential of a function and requires the use of partial derivatives if the function involves more than one dimension
force: conservative if the work done over any closed path is zero
Hooke’s law force: linear and quadratic functions of position, respectively
non-conservative force: force that does work that depends on path
conservative force: force that does work independent of path
equilibrium point: position where the assumed conservative, net force on a particle, given by the slope of its potential energy curve, is zero

Chapter 9

Linear Momentum and Collisions

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Summary

The law of conservation of momentum says that the momentum of a closed system is constant in time (conserved) Newton’s second law in terms of momentum states that the net force applied to a system equals the rate of change of the momentum that the force causes When a force is applied on an object for some amount of time, the object experiences an impulse This impulse is equal to the object’s change of momentum

Key terms

momentum: measure of the quantity of motion that an object has; it takes into account both how fast the object is moving, and its mass; specifically, it is the product of mass and…
impulse: effect of applying a force on a system for a time interval; this time interval is usually small, but does not have to be
system: object or collection of objects whose motion is currently under investigation; however, your system is defined at the start of the problem, you must keep that definition for the…
closed system: system for which the mass is constant and the net external force on the system is zero
force: applied on an object for some amount of time, the object experiences an impulse
Law of Conservation of Momentum: total momentum of a closed system cannot change
momentum of a closed system: constant in time (conserved)
perfectly inelastic: collision after which all objects are stuck together, moving with the same velocity; momentum is conserved, and the loss of kinetic energy is a maximum

Chapter 10

Fixed-Axis Rotation

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Summary

The instantaneous angular velocity of a rotating body ω = lim Δ t → 0 Δ θ Δ t = d θ d t is the derivative with respect to time of the angular position θ , found by taking the limit Δ t → 0 in the average angular… If the system’s angular velocity is not constant, then the system has an angular acceleration. The average angular acceleration over a given time interval is the change in angular velocity over this time interval, α - = Δ ω Δ t . The angular position θ of a rotating body is the angle the body has rotated through in a fixed coordinate system, which serves as a frame of reference

Key terms

given time interval: the change in angular velocity over this time interval, α - = Δ ω Δ t
angular position: angle a body has rotated through in a fixed coordinate system
instantaneous angular velocity: derivative of angular position with respect to time
angular acceleration: time rate of change of angular velocity
angular velocity: time rate of change of angular position
parallel axis: axis of rotation that is parallel to an axis about which the moment of inertia of an object is known
parallel-axis theorem: if the moment of inertia is known for a given axis, it can be found for any axis parallel to it

Chapter 11

Angular Momentum

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Summary

In rolling motion without slipping, a static friction force is present between the rolling object and the surface. The relations v CM = R ω , a CM = R α , and d CM = R θ v CM = R ω , a CM = R α , and d CM = R θ all apply, such that the linear velocity, acceleration, and distance of the center of mass are the angular variables… In rolling motion with slipping, a kinetic friction force arises between the rolling object and the surface. Energy conservation can be used to analyze rolling motion.

Key terms

angular momentum: rotational analog of linear momentum, found by taking the product of moment of inertia and angular velocity
rolling motion: combination of rotational and translational motion with or without slipping
static friction force: present between the rolling object and the surface
precession: circular motion of the pole of the axis of a spinning object around another axis due to a torque

Chapter 12

Static Equilibrium and Elasticity

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Summary

When a body in a selected inertial frame of reference neither rotates nor moves in translational motion, we say the body is in static equilibrium in this frame of reference A body is in equilibrium when it remains either in uniform motion (both translational and rotational) or at rest. Conditions for equilibrium require that the sum of all external forces acting on the body is zero (first condition of equilibrium), and the sum of all external torques from external forces is zero (second condition of… If one of them is not satisfied, the body is not in equilibrium

Key terms

equilibrium: body is in equilibrium when its linear and angular accelerations are both zero relative to an inertial frame of reference
static equilibrium: body is in static equilibrium when it is at rest in our selected inertial frame of reference
elastic: object that comes back to its original size and shape when the load is no longer present
free-body diagram for a body: a useful tool that allows us to count correctly all contributions from all external forces and torques acting on the body
body: in equilibrium when it remains either in uniform motion (both translational and rotational) or at rest
gravitational torque: torque on the body caused by its weight; it occurs when the center of gravity of the body is not located on the axis of rotation
second equilibrium condition: expresses rotational equilibrium; all torques due to external forces acting on the body balance out and their vector sum is zero
tensile strain: strain under tensile stress, given as fractional change in length, which occurs when forces are stretching an object, causing its elongation

Chapter 13

Gravitation

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Summary

The weight of an object is the gravitational attraction between Earth and the object The gravitational field is represented as lines that indicate the direction of the gravitational force; the line spacing indicates the strength of the field Apparent weight differs from actual weight due to the acceleration of the object The total energy of a system is the sum of kinetic and gravitational potential energy, and this total energy is conserved in orbital motion

Key terms

gravitational field: vector field that surrounds the mass creating the field; the field is represented by field lines, in which the direction of the field is tangent to the lines, and the magnitude…
total energy of a system: the sum of kinetic and gravitational potential energy, and this total energy is conserved in orbital motion
apparent weight: reading of the weight of an object on a scale that does not account for acceleration
weight of an object: the gravitational attraction between Earth and the object
aphelion: farthest point from the Sun of an orbiting body; the corresponding term for the Moon’s farthest point from Earth is the apogee
escape velocity: initial velocity an object needs to escape the gravitational pull of another; it is more accurately defined as the velocity of an object with zero total mechanical energy
event horizon: location of the Schwarzschild radius and is the location near a black hole from within which no object, even light, can escape
gravitationally bound: two object are gravitationally bound if their orbits are closed; gravitationally bound systems have a negative total mechanical energy

Chapter 14

Fluid Mechanics

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Summary

Absolute pressure is the sum of gauge pressure and atmospheric pressure A fluid is a state of matter that yields to sideways or shearing forces. Fluid statics is the physics of stationary fluids Pressure is the force per unit perpendicular area over which the force is applied, p = F / A .

Key terms

fluid: a state of matter that yields to sideways or shearing forces
fluids: liquids and gases; a fluid is a state of matter that yields to shearing forces
pressure: force per unit area exerted perpendicular to the area over which the force acts
absolute pressure: sum of gauge pressure and atmospheric pressure
density: mass per unit volume of a substance or object
gauge pressure: pressure relative to atmospheric pressure
SI unit of pressure: the pascal: 1 Pa = 1 N/m 2

Chapter 15

Oscillations

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Summary

Simple harmonic motion (SHM) is oscillatory motion for a system where the restoring force is proportional to the displacement and acts in the direction opposite to the displacement The time for one oscillation is the period T and the number of oscillations per unit time is the frequency f . Periodic motion is a repeating oscillation. The angular frequency ω , period T , and frequency f of a simple harmonic oscillator are given by ω = k m , T = 2 π m k , and f = 1 2 π k m , where m is the mass of the system and k is the force constant

Key terms

oscillation: single fluctuation of a quantity, or repeated and regular fluctuations of a quantity, between two extreme values around an equilibrium or average value
simple harmonic motion (SHM): oscillatory motion in a system where the restoring force is proportional to the displacement, which acts in the direction opposite to the displacement
simple harmonic oscillator: a device that oscillates in SHM where the restoring force is proportional to the displacement and acts in the direction opposite to the displacement
time for one oscillation: the period T and the number of oscillations per unit time is the frequency f
velocity: given by v ( t ) = - A ω sin ( ω t + ϕ ) = - v max sin ( ω t + ϕ ) , v ( t ) = - A ω sin ( ω t + ϕ ) = - v max sin ( ω t + ϕ ) , where v max = A ω = A k m
function of time in SHM: given by x ( t ) = A cos ( 2 π T t + ϕ ) = A cos ( ω t + ϕ ) x ( t ) = A cos ( 2 π T t + ϕ ) = A cos ( ω t + ϕ )
system where the restoring force: proportional to the displacement and acts in the direction opposite to the displacement
restoring force: force acting in opposition to the force caused by a deformation

Chapter 16

Waves

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Summary

Wave velocity and wavelength are related to the wave’s frequency and period by v = λ T = λ f Mechanical waves are disturbances that move through a medium and are governed by Newton’s laws A transverse wave has a disturbance perpendicular to the wave’s direction of propagation, whereas a longitudinal wave has a disturbance parallel to its direction of propagation A wave is a disturbance that moves from the point of origin with a wave velocity v

Key terms

wave: disturbance that moves from its source and carries energy
transverse wave: wave in which the disturbance is perpendicular to the direction of propagation
longitudinal wave: wave in which the disturbance is parallel to the direction of propagation
mechanical wave: wave that is governed by Newton’s laws and requires a medium
wave velocity: velocity at which the disturbance moves; also called the propagation velocity
wavelength: distance between adjacent identical parts of a wave
medium and: governed by Newton’s laws
constructive interference: when two waves arrive at the same point exactly in phase; that is, the crests of the two waves are precisely aligned, as are the troughs

Chapter 17

Sound

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Summary

The speed of sound depends on the medium and the state of the medium In air, the speed of sound is related to air temperature T by v = 331 m s T K 273 K = 331 m s 1 + T C 273 ° C . Sound is a disturbance of matter (a pressure wave) that is transmitted from its source outward. Sound can be modeled in terms of pressure or in terms of displacement of molecules

Key terms

sound: traveling pressure wave that may be periodic; the wave can be modeled as a pressure wave or as an oscillation of molecules
speed of sound: related to air temperature T by v = 331 m s T K 273 K = 331 m s 1 + T C 273 ° C
human ear: sensitive to frequencies between 20 Hz and 20 kHz
shock wave: wave front that is produced when a sound source moves faster than the speed of sound
transducer: device that converts energy of a signal into measurable energy form, for example, a microphone converts sound waves into an electrical signal
Doppler effect: alteration in the observed frequency of a sound due to motion of either the source or the observer
bow wake: v-shaped disturbance created when the wave source moves faster than the wave propagation speed
sound intensity level: unitless quantity telling you the level of the sound relative to a fixed standard