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Physic 1201 TEST 2 FORMULA SHEET
Vectors
magnitudeA A A
r = =
A B B A
r r r r
( A B) C A (B C )
r r r r r r
A Ax A y
r r r = +
Ax = Acos θ
Ay = Asin θ
x
y A
A
tan θ =
2 2 A = Ax +Ay
Rx = Ax +B x
R (^) y = Ay+B y
A ⋅ B= ABcos θ AB
r r
Kinematics – 1 dimension
t
x
t t
x x vave ∆
2 1
2 1
t
x v t (^) ∆
∆ → 0
lim
t
v
t t
v v aave ∆
2 1
2 1
t
v a t ∆
∆ → 0
lim
v = v 0 + at
2 0 0 2
x =x +vt+ at
2 0
2 v =v + a x−x
t
v v x x 2
0 0
Kinematics – 2 dimensions
t
r vave ∆
r
t
r v t (^) ∆
∆→
r r
0
lim
t
x v t
x ∆
∆ → 0
lim
t
y v t
y ∆
∆ → 0
lim
t
v aave ∆
r r
t
v a t (^) ∆
∆→
r r
0
lim
t
v a
x
t
x ∆
∆ → 0
lim
r
t
v a
y
t
y ∆
∆ → 0
lim
r
R
a v
2
⊥^ =
τ
π R v
Newton’s Laws
1 st: ∑ F= 0
r
2 nd: ∑ F = ma
r r
3
rd : F 12 F 21
r r =−
∑ Fx =^ max
∑ Fy =^ may
R
v F ma m
2
∑ ⊥ = ⊥^ =
w m g
r r
Forces
Fk = μ k N
Fs ≤ μ s N
Fspring =− kx
w = mg
2
1 2
r
m m Fg =G
2 E
E
R
Gm g =
Constants and Math
11 2 2
2
G Nm kg
g m s
− = ×
a
b b ac x
ax bx c
2
2
θ
θ θ
θ θ
cos
sin tan
cos /
sin /
sin cos 1
2 2
adj hyp
opp hyp
Work, Energy and Power
2
2
K = mv
W = F⋅s =Fscos θ Fs
r r
Wtot =∆K =K 2 −K 1
U (^) grav = mgh
r
GMm U (^) grav =−
2
2
U (^) spring = kx
Wgrav =−∆U grav
Wspring =−∆U spring
Emech =K+ U
Wother =∆U +∆ K
F v t
W
P = ||
Rotational Kinematics
t t t
ave ∆
θ θ θ ω
2 1
2 1
t (^) ∆ t
∆→
θ ω 0
lim
t t t
ave ∆
ω ω ω α
2 1
2 1
t ∆ t
∆→
θ α 0
lim
ω = ω 0 + α t
2 0 0 2
θ = θ + ω t + α t
2 0
2 ω = ω + α θ − θ
t 2
0 0
ω ω θ θ
Impulse, Momentum and CM
p m v
r r
J = F t −t = F∆ t
r r r ( 2 1 )
J p
r (^) r =∆
P p 1 p 2
r (^) r r = +
t
p
t
v F ma m ∆
r r r r
1 2
1 1 2 2
m m
mx m x X
1 2
1 1 2 2
m m
m y m y Y
1 2
11 2 2
m m
mv m v V
x x x
...
...
1 2
11 2 2
= m m
mv m v V
y y y
1 2
1 1 2 2
m m
ma m a A
x x x
...
...
1 2
1 1 2 2
= m m
ma m a A
y y y
∑ Fext=^ MA
r r
Rotational and Linear Motion
s = θ R
v|| = ω R
a|| = α R
R
R
v a
2
2 || ⊥ = = ω
τ = 2 π / ω
Rotational Impulse and
Momentum, Torque
L = I ω 2 L = pr⊥ =mvr⊥= m ω r ⊥
2 L m ω r
J (^) θ = Γ( t 2 −t 1 )=Γ∆ t
J (^) θ =∆ L
t
L
t
I I
ω α
Γ=Fl =Frsin θ
R
a v
2 ⊥^ =
τ
π R v
Rotational Inertia and Energy
=
n
i
I miri
1
2
2 _ 2
I (^) solid cylinder = MR
2 I (^) thin _ walled_cyl =MR
2
5
Isphere = MR
2
2
K = I ω
Equilibrium
∑ Fx =^0
∑ Fy =^0
any _ axis
1 2
1 1 2 2
w w
wx w x Xcog
...
...
1 2
1 1 2 2
= w w
w y w y Ycog
