Formulas For Calculus-based Physics 1

r r r τ ≡r ×F τ ≡ r⊥ F

K ≡ 12 mv 2

K = Iw U = mgy 1 2

2

I = mr 2 I = Icm + m d 2

U = 12 k x 2

W = F| ∆r r W = F ⋅ ∆r

G m1 m 2 U =− r r r p ≡ mv r r Lr = I w r r L ≡r ×p L = r⊥ p

W = τ ∆θ

W = − ∆U dU Fx = − dx

x = xo +vo t + 12 at 2 vo + v

x = xo +

2

2

t

= vo2 + 2 a∆ x

θ = θo + wo t + 12 a t 2

wo + w

θ = θo +

2

w = wo + a t

t

w 2 = wo + 2a ∆θ 2

v =rw at = r a

dE dt r r P = F ⋅v r r J ≡ F∆ t r r J =∆p

P≡

v = vo + a t v

W = ∆K

d 2x = − (2πf ) 2 x 2 dt

x = x max cos(2π f t ) v = −v max sin(2π f t ) a = − a max cos(2π f t )

FS = k x

Gm g= 2 r v v F = mg

L T = 2π g T = 2π

m k

1 f = T 2 ∂ 2y 1 ∂y = ∂x 2 v 2 ∂t 2

y = y max cos ( 2λπ x − 2Tπ t )

G m1 m 2 F= r2 fK = µK N

v =

λ = λf T

fs

v =

FT µ

MAX POSSIBLE

v 1 v a = ∑τ I

= µS N

µ=

m L

V

P= F A P = Po + r g h

PG = P − Po

.

m = r Av . . m1 = m2 A1v1 = A2v 2

Q = mc ∆T Q = ml ∆U = Q −W

amax = (2π f ) 2 x max

r r 1 a = ∑F m W = mg

r=m

P + 12 r v 2 + r g h = constant

v max = (2πf ) x max

2 ac = vr ac = r w 2

I = (Amplitude) fBEAT = fHIGH − fLOW v ± vR f′= f v m vS

11/5/06

2

Trigonometric Identities

(sin θ ) 2 + (cosθ ) 2 = 1 2 sin θ cosθ = sin( 2θ )

Constants

g = 9.80 N kg ag = 9.80

(near earth)

m s2

G = 6.67 × 10 −11

N ⋅ m2 kg 2

mE = 5.97 × 10 24 kg r E = 6.38 × 10 6 m I o = 1.00 × 10 −12

W m2

m vsound = 343 s 1.000 atm = 1.013 × 10 5 Pa

rwater = 1.00 × 10 3

kg m3

1.000 cal = 4.186 J

c water = 4186

J kg ⋅ C o