Introductory Mechanics Formulas Reference Sheet
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1Introductory Mechanics Formulas
GM
m
N
E
2
6
24
11
2
g =
= 9.81
= 9.81
; R
= 6.4 × 10
m ; M
= 6.0 × 10
kg ; G = 6.67 × 10
N · m
/kg
E
E
2
2
R
s
kg
E
Vector Principles
ˆ k ⇒ (A
ˆ i + A
ˆ j + A
A = A
, A
, A
) ; ∆ A ≡ A
A
; a · b = ab cos θ ; |a × b| = ab sin θ
x
y
z
x
y
z
final
initial
Kinematics
t
t
2
dr
dv
d
r
∆r
∆v
r = x ˆ i + y ˆ j ; v ≡
; a ≡
=
; x(t) = x
+
v(t )dt ; v(t) = v
+
a(t )dt ; v
≡
; a
≡
0
0
av
av
dt
dt
dt
2
∆t
∆t
0
0
Constant Acceleration Kinematics
1
1
1
2
2
2
v = v
+ at ; r = r
+ v
t +
at
; r = r
+
(v
+ v)t ; x = x
+
(v
v
)
0
0
0
0
0
0
0
2
2
2a
Rotational Kinematics
2
2
s
dθ
dω
d
θ
ds
d
s
∆θ
∆ω
θ ≡
; ω ≡
; α ≡
=
; v
=
= ωr ; a
=
= αr ; ω
≡
; α
≡
t
t
av
av
r
dt
dt
dt
2
dt
dt
2
∆t
∆t
Uniform Circular Motion
2
v
2πr
2
a
= a
=
= ω
r ; T =
cent
r
r
v
Simple Harmonic Motion
1
m
L
I
x(t) = A cos(ωt + δ) ; f =
; ω = 2πf ; T
= 2π
; T
= 2π
; T
= 2π
mass spring
pend
phys pend
T
k
g
mgD
Dynamics, Friction & Gravity
F
Gm
m
net
a
b
grav
grav
spring
= a ; F
=
F
; |f
| ≤ µ
N ; |f
| = µ
N ; F
= kx ; F
=
ˆ r
; F
= w = gm
AB
BA
s
s
k
k
ab
ab
earth,m
2
m
r
ab
Work, Energy & Momentum
1
dU
2
W
=
F · ds =
F
dx +
F
dy +
F
dz ; K =
mv
; ∆U =
W
; F
=
x
y
z
BCF
int,cons
by F
2
dx
GM m
1
2
U
=
; U
= mgy ; U
=
kx
; W
= ∆E
= ∆K + ∆U
+ ∆U
+ ∆E
+ ∆E
; f ∆s = ∆E
g
g
sp
ext
sys
g
sp
chem
therm
therm
r
2
dW
d P
P ≡
= F · v ; v
v
=
(v
v
) ; p = mv ; I =
F dt = ∆p ;
F
=
2f
1f
2i
1i
ext
dt
dt
Systems of Particles
1
rdm
r
=
m
r
;
r
=
cm
i
i
cm
M
dm
tot
Rotational Dynamics
1
dW
2
2
2
2
I =
m
r
; I =
r
dm ; I
= I
+ M h
; K =
Iω
; W
=
τ dθ = ∆K
; P =
= τ ω ; L = r × p
i
p
cm
rot
rot
i
2
dt
d L
τ = r × F ; τ = r
F ;
τ = Iα ;
τ =
; v
= rω ; a
= rα ; L = Iω
⊥
cm
cm
dt
Moments of Inertia
2
2
2
cylindrical shell: I
= M R
; disk: I
= (1/2)M R
; rod: I
= (1/12)M L
;
cm
cm
cm
2
2
solid sphere: I
= (2/5)M R
; hollow sphere: I
= (2/3)M R
cm
cm
Waves
2
2
2π
2π
∂
y
1
∂
y
ω
F
y(x, t) = A sin(kx
ωt) ; ω = 2πf =
; k =
;
=
; v
= f λ =
; v
=
wave
wave on string
2
2
2
T
λ
∂x
v
∂t
k
µ
γP
γRT
B
1
P
av
2
2
v
=
=
; v
=
; P
=
µω
A
v ; I
=
;
air
solid
av
av
2
ρ
M
ρ
2
4πr
I
W
1
12
β = (10dB) log
; I
= 10
; y
= A sin(kx) cos(ωt) ; ∆L
= mλ ; ∆L
= m +
λ
0
sw
const
dest
10
2
I
m
2
0
θ
θ
θ
+ θ
θ
+ θ
θ
θ
1
2
1
2
1
2
1
2
A sin θ
+ A sin θ
= 2A cos
sin
; A sin θ
A sin θ
= 2A cos
sin
1
2
1
2
2
2
2
2
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