PHYSICS 201 — FORMULA SUMMARY — MODULE 2 Uniform ...

PHYSICS 201 — FORMULA SUMMARY — MODULE 2 Uniform Circular Motion r 2π r r v tangential = T

€

r2 v r a radial = r r

2πR or v tangential = T

Newton's Law of Universal Gravitation

€ r mm Fgravity = G 1 2 2 r

Universal Gravitation and Weight €

m m G E2 = mg RE Kepler /Newton Law of Periods for Satellite and Planetary Motion € T2

4π 2 = r 3 GmE

Mechanical Work

and

T2

4π 2 = r 3 Gm Sun

€

r r W = Fx Δx + Fy Δy or W = F Δr cos θ

Work–Energy Theorem € 1

1

2 2 W total = ΔK = mv final − mv initial 2 2

€

or aradial =

v2 R

Gravitational Work

W gravity = mgy initial − mgy final Gravitational Potential Energy

€ ΔU gravity = mgy final − mgy initial = −W gravity Elastic Work

€ 1

1

2 2 W elastic = kx initial − kx final 2 2

Elastic Potential Energy € 1

1

2 2 ΔU elastic = kx final − kx initial = −W elastic 2 2

Conservation of Total Mechanical Energy €

ΔE = Δ(K + U gravity + U elastic ) = W nonconservative Instantaneous Power €

ΔW Δt→0 Δt

P = lim

or

P = Fx v x + Fy v y

or

r r P = F v cosθ

Simple Harmonic Motion € x(t) = Acos ωt v x (t) = −Aω sin ωt a x (t) = −Aω 2 cosωt

where

ω=

Period of an Ideal Pendulum €

T = 2π

€

L g

2π k = 2πf = T m

Density / Pressure

ρ=

m V

F p= ⊥ A

Atmospheric Pressure

€

€

1 atm = 1.013 x 10 5 Pa = 1.013 x 10 3 mbar = 760 Torr Barometric Pressure Formula € p(h) = p(h = 0) − ρgh

or

p(h< ) = p(h> ) + ρg(h> − h< )

Buoyant Force €

FB = ρ fluidVdisplaced g = mfluidg Continuity Equation (Incompressible Fluid Flow) € Δ( ρAv) = 0 ⇒ ρAv = constant

Bernoulli’s Equation € 1 Δ ( p + ρgh + ρv 2 ) = 0 ⇒ 2

€

1 2

p + ρgh + ρv 2 = constant