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Kyle D.

Constant acceleration equations

_

v= __v___{0} - v

2

Δx=v_{0} t + 1/2at^{2} : Displacement as a function of time

v=v_{0} +at : Velocity as a function of time

Average Acceleration

_

a=__Δv__ = __v___{f} - v_{i}

Δt t_{f} - t_{i}

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Average Velocity

_

v=__Δx__ =__ x___{f} - x_{i}

Δt t_{f} - t_{i}

Adding Vectors Algebraically

A_{x} = A cos (ø) = X(A cos (ø)) B_{x} = B cos (ø) = X(B cos (ø))

A_{y} = A sin (ø) = Y(A sin (ø)) B_{y} = B sin (ø) = Y(B sin (ø))

R_{x} = A_{x} + B_{x} R_{y} = A_{y} + B_{y}

Magnitude and Direction of R

Magnitude of R=sqrt of R_{x}^{2} + R_{y}^{2}

Direction of R: ø=tan^{-1} (__R___{y} )

(R_{x} )

Displacement, average Velocity, average Acceleration of an object

ΔR≡R_{f} - R_{i} V_{avg} ≡ __ΔR__ A_{avg} ≡ __ΔV__

Δt Δt

Work

W=FΔx

SI unit: joule=newton x meter=kg m^{2} /s^{2} and is a scalar quantity

W≡(F cos θ) Δx

Work done by friction

W_{fric} = -μ_{k} mgΔx W_{fric} = -μ_{k} (mg - F_{applied} sinθ)Δx

W_{net} = W_{applied} + W_{friction} + W_{n} + W_{g : N and G are not applied when perpindicular.}

Kinetic Energy

KE=1/2mv^{2} measured in joules and IS A SCALAR

W_{net} =KE_{f} - KE_{i} = ΔKE

Average angular speed

ω_{avg} = __Δθ__ units: radians/second rev/s • __2π rads__

Δt rev

Angular acceleration

a_{avg} = __Δω__ SI unit: radians/second^{2} positive in counterclockwise direction.

Δt

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Rotational Motion

ω=ω_{i} + at

Δθ=ω_{i} t + 1/2 at^{2}

ω^{2} = ω_{i}^{2} +2aΔθ

Tangential speed and acceleration

v_{t} = rω

a_{t} = ra

Centripetal Acceleration and total acceleration

a_{c} = __v____2 __ = rω^{2 } a= sqrt:a_{t}^{2} + a_{c}^{2}

r

Newtons Law of universal gravitation

F=G __m___{1}__ m___{2} G=6.673 x 10^{-11} N•m^{2} /kg^{2} r^{2}

_{}

Kepler's Law, eliptical orbits of planets

T^{2} = (4π^{2} / GM_{s} )r^{3} where M_{s} is mass of sun or other central located body.

Torque

Moment of Inertia

Conservation of Angular Momentum

Density

ρ = m / v SI unit: kg/m^{3 } v = π r^{2} h

Pressure

P = F / A SI unit: Pascal; Pa; newtons per square meter

Area of rectangle= length x width

P=P_{o} (atmospheric pressure) + pgh

Bernoullis equation

P + 1/2ρv^{2} + 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

B=ρ_{fluid}V_{fluid}g

Temperature

T_{c} = 5/9(T_{f} - 32)

T_{k} = T_{c + 273.15}

Thermal Expansion

ΔL= α L_{0} ΔT where α equals the coefficient of linear expansion.

Coefficient of volume expansion

ΔV=βV_{0} ΔT where β equals (3α)

Coefficient of area expansion

ΔA=γA_{0} ΔT where γ equals (2α)

Radiation, Conduction and Convection

The Unusual Behavior of Water

Avogadro’s number

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

Length

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

Area

square kilometer (km2

) = 100 hectares 1 km2

= 0.386 mi

2

1 mi

2

= 2.590 km2

hectare (ha) = 10,000 m2

1 ha = 2.471 acres 1 acre = 0.405 ha

square meter (m2

) = 10,000 cm2

1 m2

= 10.765 ft

2

1 ft

2

= 0.093 m2

square centimeter (cm2

) = 100 mm2

1 cm2

= 0.155 in.

2

1 in.

2

= 6.452 cm2

Volume

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

Mass

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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