D&R 1 Flashcards
What are the unit vectors?
i = (100) j = (010) k = (001)
What is the relationship for vector distance r?
r(t) = r(t0) + (t-t0) v(t0) + 1/2 a (t-t0)^2
(s = ut + 1/2at^2)
What are the calculus relationships of a, v & x?
v = dx/dt
a = dv/dt = d^2x/dt^2
x = § v dt
What are the relationships for horizontal velocity?
v(x) = v(x0) + a(x) (t - t0)
(v = u + at)
v(x)^2 = v(x0)^2 + 2a (x - x0)
(v^2 = u^2 + 2as)
What is the relationship for horizontal displacement?
x - x0 = v(x0) (t - t0) + 1/2 a(x) (t - t0)^2
(s = ut + 1/2 at^2)
What is the equation for vertical velocity?
v(y) = v(y0) - g(t - t0)
[a = -g /+ \/-]
(v = u + at)
What is the relationship for vertical displacement?
y - y(0) = v(y0) (t - t0) - 1/2 g (t - t0)^2
What is the relationship for the total initial velocity?
v(0) = _/ v(x0)^2 + v(y0)^2 at tan^-1(v(y0)/v(x0))
What are the relationships for the initions horizontal and vertical components of velocity?
v(x0) = v(0) cos •
v(y0) = v(0) sin •
How do we find the maximum horizontal displacement?
y = x(v(y0)/v(x0)) - x^2(g/(2 v(x0))^2)
0 = (v(y0)/v(x0)) - x(g/(2 v(x0))^2)
x = (2 v(x0) v(y0))/g
How do we find the maximum vertical displacement?
y = x’(v(y0)/v(x0)) - x’^2(g/(2 v(x0))^2)
y = (v(y0)^2)/2g
What are the relationships between linear and angular displacement
(x,y) ≈ (r,•)
x = r cos• y = r sin•
r = _/x^2 + y^2 • = tan^-1(y/x)
What is the relationship for the period of rotation?
T = 2pi/w
What is the relationship between liner and angular velocity?
v = wr
What is the relationship for radial acceleration?
a(rad) = w^2r = v^2/r
What is the relationship for rotational tension?
T = m a(rad) = m v^2/r
(w = _/T/mr)
What is the relationship for rotational tension at an angle?
mg = Tsin•
Tcos• = mw^2rcos•
g = w^2rsin•
sin• = g/w^2r
What is the relationship for Gravitational Force?
F = Gm1m2/r^2
What is the relationship for gravitational field strength?
g = _/2GM
What is the relationship for maximum height?
h = _/Gm1m2/F
What is the definition of Simple Harmonic Motion?
Oscillation of a mass about an equilibrium (0)
What is the relationship for force in a spring?
F = -kx
What is the relationship for angular frequency of a mass on a spring?
w = _/k/m
What is the relationship for the displacement from 0?
x = Acos(wt + •)
What is the equation for the velocity in x?
v(x) = -wAsin(wt + •)
What is the relationship for the acceleration?
a = -(k/m)x
What is the relationship for the initial velocity?
v(0) = -Awsin(•)
What is the relationship for the initial displacement?
x(0) = Acos(•)
What is the relationship for amplitude?
A = _/x(0)^2 + (v(0)/w)^2
What is the relationship for •
• = tan^-1(v(0)/wx(0)) - wt(0)
What is the relationship for the change in length of the spring?
k DL = mg
What is the small angle approximation?
sin• = •
What is the relationship for the normal force of a pendulum?
n = mgcos•
What is the relationship for the velocity of a pendulum?
v = l d•/dt
What is the relationship for the acceleration of a pendulum?
a = gsin•
What is the relationship for the angular velocity of a pendulum?
w = _/g/l
What is the relationship for the frictional force in a pendulum?
Fs= mgsin • = us n = us mgcos•
What is the relationship for the coefficient of frictional force of a pendulum?
us = tan(•)
