Chapter 1-3

Question 1

Vector

Answer 1

quantity with magnitude and direction (ex: velocity)

Question 2

Scalar

Answer 2

quantity with magnitude only (ex: mass)

Question 3

Unit Vector

Answer 3

vector with a magnitude of one that is used to specify a direction in space

Question 4

Direction Angles

Answer 4

(alpha, beta, gamma) angles that a vector makes with x, y, and z axes

Question 5

Direction Cosines

Answer 5

another way to specify direction of a vector (nhat = cos(alpha)ihat + cos(beta)jhat + cos(gamma)khat

Question 6

Dot Product / Scalar Product

Answer 6

A dot B = ABcos(theta) which makes a scalar

Question 7

Cross Product / Vector Product

Answer 7

A cross B = ABsin(theta) which makes a vector

Question 8

Triple Vector Product

Answer 8

A cross (B cross C) = B(A dot C) - C(A dot B) “Back Minus Cab Rule”

Question 9

Position Vector (r)

Answer 9

vector from the origin to point P

Question 10

Displacement Vector (delta r)

Answer 10

vector from an initial point P to a final point P’

Question 11

Velocity

Answer 11

the rate of change of displacement with respect to time

Question 12

Acceleration

Answer 12

rate of change of velocity with respect to time

Question 13

Mechanics

Answer 13

the study of motion

Question 14

Kinematics

Answer 14

description of an object’s motion without regard to the causes of the motion

Question 15

Dynamics

Answer 15

study of the causes of motion (forces)

Question 16

Force

Answer 16

any influence that can cause an object to accelerate

Question 17

Net Force

Answer 17

vector sum of all forces acting on an object simultaneously

Question 18

Goal of Classical Mechanics

Answer 18

to determine the future state of an object based on an understanding of its present state and the forces that are acting on it

Question 19

Newton’s 1st Law of Motion

Answer 19

(“Law of Inertia”) an object will remain at rest or continue moving at a constant speed in a straight line unless a net force acts on it (Fnet = 0 so v = constant)

Question 20

Inertia

Answer 20

an object’s resistance to having its motion changed

Question 21

Mass

Answer 21

(m) a measure of an object’s inertia (amount of matter in an object)

Question 22

Newton’s 2nd Law of Motion

Answer 22

if a net force acts on an object, the object will accelerate. The acceleration is directly proportional to the net force, inversely proportional to the mass, and direction of net force (Fnet = dp/dt or Fnet = ma for constant mass)

Question 23

Newton’s 3rd Law of Motion

Answer 23

when object 1 exerts a force on object 2 (F12), object 2 exerts an equal force in opposite direction on object 1 (F21) (F12 = -F21)

Question 24

Constant Acceleration Equations

Answer 24

v = v0 + at
x = x0 + v0t + 0.5at^2
v^2 = v0^2 + 2a(x-x0)

Question 25

Free-Body Diagram

Answer 25

picture showing all forces acting on an object

Question 26

Kinetic Energy

Answer 26

(T) energy due to a particle’s motion (T = 0.5mv^2)

Question 27

Energy

Answer 27

ability to do work

Question 28

Work

Answer 28

(W) product of an object’s displacement (caused by force) with the component of force in direction of displacement (W = integral from x0 to x of F dot dx)

Question 29

Potential Energy

Answer 29

(v) energy due to a particle’s position

F(x) = -dV(x)/dx

Question 30

Total Energy

Answer 30

(E) sum of a particle’s kinetic and potential energies

E = T + V

Question 31

Law of Conservation of Energy

Answer 31

energy cannot be created or destroyed. It can be transformed from one type to another, but the total energy of a closed system must remain constant

Question 32

Turning Points

Answer 32

at points E = V(x), the object stops (v = 0) and reverses its motion

Question 33

Oscillation

Answer 33

vibration that remains stationary in space

Question 34

Wave

Answer 34

vibration that travels through space

Question 35

Period

Answer 35

(T) time for 1 complete oscillation (or cycle)

Question 36

Frequency

Answer 36

(f) number of oscillations (or cycles) per second

f = 1/T

Question 37

Angular Frequency

Answer 37

(omega) number of radians per second

omega = 2pi*f

Question 38

Amplitude

Answer 38

(A) distance from the midpoint of an oscillation to one extreme

Question 39

Hooke’s Law

Answer 39

the force exerted by a spring is linearly proportional to the displacement from equilibrium position and in the opposite direction
F = -kx

Question 40

Simple Harmonic Motion

Answer 40

oscillatory motion that occurs when a system moves in response to a restoring force that is linearly proportional to the system’s displacement from equilibrium

1. x(t) = Be^(iomegat) + Ee^(-iomegat)
2. x(t) = Ccos(omegat) + Dsin(omegat)
3. x(t) = Asin(omega*t + phi)

Question 41

Damped Harmonic Oscillator

Answer 41

harmonic oscillator that includes a frictional force

F = -c(dx/dt)

Question 42

Overdamped

Answer 42

(q is real) large damping force, a displaced mass released from rest returns to equilibrium slowly and does not oscillate
x(t) = Ae^-(gamma - q)t + Be^-(gamma + q)t

Question 43

Critically damped

Answer 43

(q = 0) special damping, a displaced mass released from rest returns to equilibrium the fastest and does not oscillate
x(t) = (A + B)e^(-gamma*t)

Question 44

Underdamped

Answer 44

(q is imaginary) small damping force, a displaced mass released from rest undergoes SHM at a frequency of omega sub d rather than omega sub not, but oscillation is killed by the exponential term
x(t) = e^(-gammat)[Asin(omegadt + phi)]

Question 45

Forced Harmonic Oscillator

Answer 45

damped harmonic oscillator that includes a sinusoidal driving force
F = F0cos(omega*t)

Question 46

Resonance Frequency

Answer 46

(omega sub r) driving force frequency that causes a huge maximum in the oscillation’s amplitude
omegar = sqrt(omega0^2 - 2*gamma^2)

Question 47

Quality Factor

Answer 47

(Q) parameter characterizing the rate of energy loss in a weakly damped oscillator
Q = omegad/(2*gamma)