Chapter 1-3 Flashcards
Vector
quantity with magnitude and direction (ex: velocity)
Scalar
quantity with magnitude only (ex: mass)
Unit Vector
vector with a magnitude of one that is used to specify a direction in space
Direction Angles
(alpha, beta, gamma) angles that a vector makes with x, y, and z axes
Direction Cosines
another way to specify direction of a vector (nhat = cos(alpha)ihat + cos(beta)jhat + cos(gamma)khat
Dot Product / Scalar Product
A dot B = ABcos(theta) which makes a scalar
Cross Product / Vector Product
A cross B = ABsin(theta) which makes a vector
Triple Vector Product
A cross (B cross C) = B(A dot C) - C(A dot B) “Back Minus Cab Rule”
Position Vector (r)
vector from the origin to point P
Displacement Vector (delta r)
vector from an initial point P to a final point P’
Velocity
the rate of change of displacement with respect to time
Acceleration
rate of change of velocity with respect to time
Mechanics
the study of motion
Kinematics
description of an object’s motion without regard to the causes of the motion
Dynamics
study of the causes of motion (forces)
Force
any influence that can cause an object to accelerate
Net Force
vector sum of all forces acting on an object simultaneously
Goal of Classical Mechanics
to determine the future state of an object based on an understanding of its present state and the forces that are acting on it
Newton’s 1st Law of Motion
(“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)
Inertia
an object’s resistance to having its motion changed
Mass
(m) a measure of an object’s inertia (amount of matter in an object)
Newton’s 2nd Law of Motion
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)
Newton’s 3rd Law of Motion
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)
Constant Acceleration Equations
v = v0 + at x = x0 + v0t + 0.5at^2 v^2 = v0^2 + 2a(x-x0)
Free-Body Diagram
picture showing all forces acting on an object
Kinetic Energy
(T) energy due to a particle’s motion (T = 0.5mv^2)
Energy
ability to do work
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)
Potential Energy
(v) energy due to a particle’s position
F(x) = -dV(x)/dx
Total Energy
(E) sum of a particle’s kinetic and potential energies
E = T + V
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
Turning Points
at points E = V(x), the object stops (v = 0) and reverses its motion
Oscillation
vibration that remains stationary in space
Wave
vibration that travels through space
Period
(T) time for 1 complete oscillation (or cycle)
Frequency
(f) number of oscillations (or cycles) per second
f = 1/T
Angular Frequency
(omega) number of radians per second
omega = 2pi*f
Amplitude
(A) distance from the midpoint of an oscillation to one extreme
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
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
- x(t) = Be^(iomegat) + Ee^(-iomegat)
- x(t) = Ccos(omegat) + Dsin(omegat)
- x(t) = Asin(omega*t + phi)
Damped Harmonic Oscillator
harmonic oscillator that includes a frictional force
F = -c(dx/dt)
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
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)
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^(-gammat)[Asin(omegadt + phi)]
Forced Harmonic Oscillator
damped harmonic oscillator that includes a sinusoidal driving force
F = F0cos(omega*t)
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)
Quality Factor
(Q) parameter characterizing the rate of energy loss in a weakly damped oscillator
Q = omegad/(2*gamma)
