Science Equations

2/20/2014

Frequently Used Equations - The Physics Hypertextbook

Frequently Used Equations
Mechanics
velocity
Δ
s v= Δ t ds v= dt

acceleration
Δ
v a= Δ t dv a= dt

equations of motion v = 0+at v x =x0+v 0 +½ 2 t at

weight
W =m g

momentum p =m v

dry friction ƒ μ
=N

centrip. accel. v2 ac = r 2 ac =−ω r

impulse
J =F Δ t impulse–momentum
F Δ= Δ t m v

J =⌠ dt
F

⌠ dt =Δ
F
p
⌡

kinetic energy

potential energy

⌡

K =½ mv 2

gravitational p.e.
Δ g =mgΔ
U
h

Δ =−⌠ ·
U
F ds

⌡

F =−∇U

v 2= 0 +2 x − 0 v 2 a( x ) v =½ v + 0
( v)

work
W = s cs
FΔ o θ
W =⌠ ·
F ds

newton's 2nd law
∑F =m a dp ∑F = dt efficiency
Wout
ℰ=
Ein

work–energy
FΔ cs =Δ s oθ E

⌡

⌠ · =Δ
F ds
E
⌡

power
Δ
W
P=
Δ t P = cs
Fv o θ

dW
P=
dt
P =F · v angular velocity
Δ
θ ω= Δ t dθ ω= dt v =ω ×r

angular acceleration
Δ
ω α= Δ t dω α= dt
2
a = × −ω r α r

equations of rotation ω=ω +α t 0 θ θ +ωt +½ t2
=0 0 α torque τ rF s θ
=
i n τ =r ×F

moment of inertia
I =∑mr2

rotational work
W =τ θ
Δ

I = r2dm

W= τ· dθ rotational k.e.
K =½ 2
Iω

angular momentum
L =mrv s θ i n
L =r ×p

hooke's law
F =− Δ k x

L= ω
I

frequency
1
ƒ
=
T ω=2ƒ π

universal gravitation
Gm m
Fg =− 1 2r̂ r2 gravitational field
Gm
g =− 2 r̂ r gravitational p.e.
Gm m
Ug =− 1 2 r gravitational potential
Gm
Vg =− r orbital speed
Gm
v =√ r escape speed
2
Gm v =√ r s.h.o. m T =2 √ π k

simple pendulum
ℓ
T =2 √ π g

density

pressure

pressure in a fluid

buoyancy

http://physics.info/equations/

⌠
⌡

2 ω =ω2+2( −θ αθ 0
)
0 ω=½ ω+ω)
(
0

⌠
⌡

2nd law for rotation
∑τ = α
I
dL
∑τ = dt rotational power
P =τ cs ω oθ
P =τ · ω elastic p.e.
Us =½ x2 kΔ 1/5

2/20/2014

Frequently Used Equations - The Physics Hypertextbook

m ρ =