PHYS 211
Equation Sheet
̂
∙
| |
̂
cos
c = ab sin( ); direction: RHR
̂
̂
Δ
Δ
d
d
d
̂
̂
d
d
d
for
̂
Δ
Δ
̂
d
d
Δ
∙
d
̂
d
Δ
Δ
Δ
Δ
,
at = r 
1
Δ
2
(constant mass)
Δ
Δ
fs ≤ s n
̂
;
1
2
1
2
⋅d
Δ
d
Δ
∙
Wnc = Wext + Wdiss
d
;
1D Elastic
Collisions
∑
∑
1
2
fk = k n
;
d
̂
Emech;i + Wext = Emech;f + Eth
Δ
Δ
2
;
2
;
;
;
;
or
or
x(t) = Acos(t + 0)
2
1
Δ
2
If is Conservative
Δ ≡
̂
Fixed Axle:
I = ICoM + Md2
sin
Δs
Δ
Eth = fk d = –Wdiss
≡
d
1
2
d
d
Emech = U + K
2
2 Δ
Ug = mgy
⋅Δ
,
̂
2 Δ
2 Δ
2 Δ
,
s = r 
≡
̂
̂
,
1
2
d
d
v(t) = –A sin(t + 0)
2
a(t) = –A 2cos(t + 0)
2
1
12
1
12
Moments of Inertia (for uniform density) about center of mass
1
2
Spheres:
Constant
acceleration due to gravity
(Earth)
gravitational constant
radius of the earth
mass of the Earth
Prefix
femtopiconanomicromillicentikilomegagiga-
Letter
f
p
n

m
c
k
M
G
Symbol
g
2
5
2
3
Value
9.80 m/s2
6.67 × 10–11 N m2 / kg2
6.37 × 106 m
5.98 × 1024 kg

3.14159

Unit Conversions
Unit Comparisons
–10
1 Å = 10 m
1 N = 1 kg m / s2
1 inch = 2.54 cm
1J=1Nm
1 mile = 1609 m
1W=1J/s
1 m/s = 2.24 mph
G
RE
Meaning
10–15
10–12
10–9
10–6
10–3
10–2
103
106
109
1 Hz = 1 s–1 = 60 rpm
1 rev = 2 rad = 360°
1 lb = 4.45 N
1 u = 1.66 × 10–27 kg
If:

a x2 + b x + c = 0,
then
C
A
A2 + B2 = C2

B
Angle
Sine
deg
rad
30°
1/2
/6
45°
/4
√2/2
60°
/3
√3/2
sin
sin
cos
for constants a, c and
n
Cosine
√3/2
√2/2
1/2
cos
Tangent
√3/3
1
√3
sin
 b  b 2  4 ac
2a
SOHCAHTOA
A
A
sin( )  cos( ) 
tan( ) 
C
B
B
B
cos( )  sin( ) 
tan( ) 
C
A
sin
sin
sin
x

a

c

b
cos
cos
a2 = b2 + c2 – 2 b c cos()
b2 = a2 + c2 – 2 a c cos()
c2 = a2 + b2 – 2 a b cos()
cos
∓ sin
sin
′
0
cos
sin
sin
cos
(n ≠ –1)
tan
sec