Chapter 1-3 Flashcards

1
Q

Vector

A

quantity with magnitude and direction (ex: velocity)

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2
Q

Scalar

A

quantity with magnitude only (ex: mass)

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3
Q

Unit Vector

A

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

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4
Q

Direction Angles

A

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

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5
Q

Direction Cosines

A

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

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6
Q

Dot Product / Scalar Product

A

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

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7
Q

Cross Product / Vector Product

A

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

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8
Q

Triple Vector Product

A

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

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9
Q

Position Vector (r)

A

vector from the origin to point P

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10
Q

Displacement Vector (delta r)

A

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

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11
Q

Velocity

A

the rate of change of displacement with respect to time

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12
Q

Acceleration

A

rate of change of velocity with respect to time

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13
Q

Mechanics

A

the study of motion

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14
Q

Kinematics

A

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

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15
Q

Dynamics

A

study of the causes of motion (forces)

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16
Q

Force

A

any influence that can cause an object to accelerate

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17
Q

Net Force

A

vector sum of all forces acting on an object simultaneously

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18
Q

Goal of Classical Mechanics

A

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

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19
Q

Newton’s 1st Law of Motion

A

(“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)

20
Q

Inertia

A

an object’s resistance to having its motion changed

21
Q

Mass

A

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

22
Q

Newton’s 2nd Law of Motion

A

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)

23
Q

Newton’s 3rd Law of Motion

A

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)

24
Q

Constant Acceleration Equations

A
v = v0 + at
x = x0 + v0t + 0.5at^2
v^2 = v0^2 + 2a(x-x0)
25
Free-Body Diagram
picture showing all forces acting on an object
26
Kinetic Energy
(T) energy due to a particle's motion (T = 0.5mv^2)
27
Energy
ability to do work
28
Work
(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)
29
Potential Energy
(v) energy due to a particle's position | F(x) = -dV(x)/dx
30
Total Energy
(E) sum of a particle's kinetic and potential energies | E = T + V
31
Law of Conservation of Energy
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
32
Turning Points
at points E = V(x), the object stops (v = 0) and reverses its motion
33
Oscillation
vibration that remains stationary in space
34
Wave
vibration that travels through space
35
Period
(T) time for 1 complete oscillation (or cycle)
36
Frequency
(f) number of oscillations (or cycles) per second | f = 1/T
37
Angular Frequency
(omega) number of radians per second | omega = 2pi*f
38
Amplitude
(A) distance from the midpoint of an oscillation to one extreme
39
Hooke's Law
the force exerted by a spring is linearly proportional to the displacement from equilibrium position and in the opposite direction F = -kx
40
Simple Harmonic Motion
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^(i*omega*t) + Ee^(-i*omega*t) 2. x(t) = Ccos(omega*t) + Dsin(omega*t) 3. x(t) = Asin(omega*t + phi)
41
Damped Harmonic Oscillator
harmonic oscillator that includes a frictional force | F = -c(dx/dt)
42
Overdamped
(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
43
Critically damped
``` (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) ```
44
Underdamped
(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^(-gamma*t)[Asin(omegad*t + phi)]
45
Forced Harmonic Oscillator
damped harmonic oscillator that includes a sinusoidal driving force F = F0cos(omega*t)
46
Resonance Frequency
(omega sub r) driving force frequency that causes a huge maximum in the oscillation's amplitude omegar = sqrt(omega0^2 - 2*gamma^2)
47
Quality Factor
(Q) parameter characterizing the rate of energy loss in a weakly damped oscillator Q = omegad/(2*gamma)