Vectors:
A = Ax xˆ + Ay yˆ + Az zˆ
A = A = Ax2 + Ay2 + Az2
(
C y = A y + By
C = A + Bx
x x
A ⋅ B = Ax B x + Ay B y + Az B z = AB cos θ
Kinematics:
Constant
acceleration:
)
1
2
a
aˆ = a
Cz = Az + Bz
r = xxˆ + yyˆ
dr
v=
= vx xˆ + v y yˆ
dt
dv
a=
= ax xˆ + a y yˆ
dt
∆r = rf − ri
∆r
< v >=
∆t
∆v
< a >=
∆t
1
x = xo + voxt + ax t 2
2
Earth’s gravity:
g = 9.8 m/sec2
vx = vox + axt
vx2 = vox2 + 2ax ( x − xo )
< vx >=
Uniform
circular
motion:
v2
ar =
r
Quadratic
formula
x=
v f + vi
x − xo =< vx > ∆t
2
− b ± b 2 − 4ac
2a
Newton’s
2nd Law
Fx = max
Friction
Ff = µN
Restoring
Force
(Hooke’s
Law)
Fs = k(l - lo)
Fy = may
Fx = kx
5
Fz = maz
Work &
Energy
Mechanical
Energy
Impulse &
Momentum
Rocket
Universal
Gravitation
W = F⋅d⋅cos(θ)
Wtotal = ∆K;
Wconservative = -∆U
∆Ug = mg∆y
or
U = mgh
E=K+U
∆E = Wnonconservative = ∆I
J = F ⋅ ∆t = ∆p
p = m⋅v
vector version
dv dm
Fext = m
+V
dt
dt
dm
>0
dt
Fg =
G⋅M ⋅m
r2
G = 6.67 × 10 −11
N ⋅ m2
kg 2
6
1 2
mv
2
1
2
k (l − l o )
2
1
= kx 2
2
∆U spring =
∆U spring
No external force :
p final = p initial
one dimensional
as in the text
dm
ve > 0 ;
<0
dt
Ug = −
K=
G⋅M ⋅m
r
Fext , x = m
ve =
dv x
dm
+ ve, x
dt
dt
2GM
R