Wnet = Wapplied + Wfriction + Wn + Wg : N and G are not applied when perpindicular.
KE=1/2mv2 measured in joules and IS A SCALAR
Wnet =KEf - KEi = ΔKE
Average angular speed
ωavg = Δθ units: radians/second rev/s • 2π rads
aavg = Δω SI unit: radians/second2 positive in counterclockwise direction.
ω=ωi + at
Δθ=ωi t + 1/2 at2
ω2 = ωi2 +2aΔθ
Tangential speed and acceleration
vt = rω
at = ra
Centripetal Acceleration and total acceleration
ac = v2 = rω2 a= sqrt:at2 + ac2
Newtons Law of universal gravitation
F=G m1 m2 G=6.673 x 10-11 N•m2 /kg2
Kepler's Law, eliptical orbits of planets
T2 = (4π2 / GMs )r3 where Ms is mass of sun or other central located body.
T=Iα SI unit = N•m
T = rF(sin θ)
Moment of Inertia
I = mr2 / 2
Conservation of Angular Momentum
Ii ωi= If ωf
ρ = m / v SI unit: kg/m3 v = π r2 h
P = F / A SI unit: Pascal; Pa; newtons per square meter
Area of rectangle= length x width
P=Po (atmospheric pressure) + pgh
P + 1/2ρv2 + ρgy
Stress and Strain modulus
Stress is related to the force per unit area producing a deformation; strain (dimensionless) is the measure of of the amount of deformation. (elastic modulus) Stress=elastic modulus • strain.
Youngs modulus: resistance of solid to elongation or compression, Y.
Shear modulus: resistance to displacement of faces of solids sliding past eachother, S.
Bulk modulus: the resistance of solid or liquid to change in volume, B.
Archimede's principle, bouyancy
Tc = 5/9(Tf - 32)
Tk = Tc + 273.15
ΔL= α L0 ΔT where α equals the coefficient of linear expansion.
Coefficient of volume expansion
ΔV=βV0 ΔT where β equals (3α)
Coefficient of area expansion
ΔA=γA0 ΔT where γ equals (2α)
Radiation, Conduction and Convection
The Unusual Behavior of Water
temperature increases from 0°C to 4°C, water contracts, so its density increases. Above 4°C, water exhibits the expected expansion with increasing temperature. The density of water reaches its maximum value of 1 000 kg/m3 at 4°C.
NA= 6. 02x 10 ^23 particles/ mole
ideal gas law
PV= nRT R= 8.3 1 J/ mol • K R = 0.082 1 L • atm / mol • K
1 cal 4. 186 J
kilometer (km) = 1,000 m 1 km = 0.621 mi 1 mi = 1.609 km
meter (m) = 100 cm 1 m = 3.281 ft 1 ft = 0.305 m
centimeter (cm) = 0.01 m 1 cm = 0.394 in. 1 in. = 2.540 cm
millimeter (mm) = 0.001 m 1 mm = 0.039 in.
micrometer (µm) = 0.000 001 m
nanometer (nm) = 0.000 000 001 m
square kilometer (km2
) = 100 hectares 1 km2
= 0.386 mi
= 2.590 km2
hectare (ha) = 10,000 m2
1 ha = 2.471 acres 1 acre = 0.405 ha
square meter (m2
) = 10,000 cm2
= 10.765 ft
= 0.093 m2
square centimeter (cm2
) = 100 mm2
= 0.155 in.
= 6.452 cm2
liter (L) = 1,000 mL = 1 dm3
1 L = 1.057 fl qt 1 fl qt = 0.946 L
milliliter (mL) = 0.001 L = 1 cm3
1 mL = 0.034 fl oz 1 fl oz = 29.575 mL
microliter (µL) = 0.000 001 L
kilogram (kg) = 1,000 g 1 kg = 2.205 lb 1 lb = 0.454 kg
gram (g) = 1,000 mg 1 g = 0.035 oz 1 oz = 28.349 g
milligram (mg) = 0.001 g
microgram (µg) = 0.000 001 g
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