Navy OAR Formulas

Rate, Distance, Time

r = D/T (or D = RT, T = D/r)

Quadratic Formula

x = (-b ± √(b² - 4ac)) / (2a)

Slope of a Line

m = (y2 - y1) / (x2 - x1)

Slope-Intercept Form

y = mx + b

Simple Interest

I = Prt

Mean

sum of data / number of data entries

Midpoint Formula

M = ((x1 + x2) / 2, (y1 + y2) / 2)

Velocity/Acceleration

d = 1/2 at² (Distance = 1/2 Acceleration × Time²)

Mechanical Advantage (General)

MA = Load Force / Effort Force

Gears

R1D1 = R2D2 (Revolutions × Teeth)

Torque

t = Force × Distance

Pressure

Pressure = Force / Area

Lever (First Class)

Force1 × Distance1 = Force2 × Distance2

Inclined Plane (MA)

Length of Slope ÷ Height of Slope

Wheel and Axle (MA)

Radius of Wheel ÷ Radius of Axle

Electrical Power

P = Work / Time

Ohm's Law

V = I × R (Voltage = Current × Resistance)

Circle Area

A = πr²

Circle Circumference

C = 2πr (or C = πd)

Rectangular Solid Volume

V = lwh

Rectangular Solid Surface Area

SA = 2(lw + wh + lh)

Triangle Area

A = 1/2 × base × height

Pythagorean Theorem

a² + b² = c²

Trapezoid Area

A = 1/2 h(b1 + b2)

Cylinder Volume

V = πr²h

Cylinder Surface Area

SA = 2πrh + 2πr²

Sphere Volume

V = (4/3)πr³

Sphere Surface Area

SA = 4πr²

Revolutions

R = 2π radians

Total # of Degrees

180(#of sides-2)

Distance Formula

Power and Roots

Multiply: x²*x³=x⁵

Raising Power: (x²)³=x⁶

Multiply Square Roots: 3√5*7√2=21√10

Sum of all Angles

180(N-2)

Perimeter of a Rectangle

P = 2L + 2W

Perimeter of a Square

P = 4S

Area of a Rectangle

A = lw

Area of a Square

A = s²

Area of a Parallelogram

A = bh

Area of a Triangle

A = bh/2

Area of a Trapezoid

A = ½ (b₁+b₂) x h

Area of a Circle

A = πr²

Circumference of a Circle

c = πd (diameter)

Volume of a Rectangular Solid

V = lwh

Volume of a Cube

V = s³

Volume of a Cylinder

V = πr²h

Volume of a Pyramid

V = 1/3lwh

Surface Area of a Cube

6a²

Surface Area of a Prism

2ab + 2bc + 2ac

Surface Area of a Sphere

4πr²

Surface Area of a Cylinder

2πr² + 2πrh

Calculating Percentages

part/whole = %/100

Equation of Velocity?

Distance/Time (d/t)

Formula for Momentum?

Mass x Velocity (v/t)

What is the Equation for Force?

Mass x Acceleration (M x A)

Average Velocity

position/time = displacement/time

Ave. Acceleration

Velocity/Time

Mechanical Advantage

output force/input force = MA

Maximum Weight Questions

Force x Mechanical Advantage = MW

Force Necessary Questions

Weight/MA

Mechanical Advantage of an incline plane

length/height = MA

Determining:

Net Force

Gravitational Force

Frictional Force

Acceleration

Net Force = M x A

Grav Force = M x G

Fric Force =

Acceleration

a = Fnet/M

Efficiency and Work Formula

WORKout/WORKin

this fraction can never be greater than 1

Work= Force x Distance

to solve force, displacement and angle must be know.

Voltage

Current x Resistance =

Mechanical Advantage for Levers

Divide:

Length of Effort Arm

_______________

Length of Load (or resisting arm)

Lever Formula

Weight x Distance = Weight x Distance

d1 d2

__________________

w1 /\ w2

MA for Gears

# of teeth in the driven or load gear

___________________

# of teeth in the effort of driver gear

Number of Revolutions

r = (D x R)/d

r = #rev A

d= # teeth A

D=#rev B

R=#rev B

MA of a Pulley

MA = # of strands

Force of a Pulley

weight/# of strands

Pressure Formula

Pressure = Force / Area

Piston Formula

a2/a1 = d1/d2

* Remember to multiply the MA by the vertical distance moved by the piston a to find the vertical distance moved by piston b

A x D = a x d

A and D are larger areas and a and d are the smaller

MA of Inclined Plane

Length of the Ramp

_______________

Hight of the Ramp

Smaller rope equals greater MA

Wheel and Axel

MA = diameter of wheel

___________

diameter of axle

What is the equation for velocity?

distance/time

How do I find lengths in a right triangle?

a^2+b^2=c^2

What is momentum?

mass x velocity

What is the equation for force?

Force = mass x acceleration

Pressure Equation

Pressure = force/area

Work Equation

Work(w) = Force(f) x Distance(d)

Percent change equation

amount of change / original amount

(a^m)*(a^n) =

a^(m+n)

(a^m)^n=

a^(mn)

linear line equation

y = mx + b

equation to find the area of a shade in a circle

(Angle/360) (Pi) (r^2)

how to find the angle in a circle

S = (angle/360) * 2PiR

Percent Change

Percent / 100 = Difference / Original Number

Percent of a Number

Percent / 100 = Part / Whole

Boyle's Law

P1V1=P2V2

Charle's Law

V1/T1=V2/T2

Avogadro's Law

V1/n1=V2/n2

Rectangular Prism Volume

V=ℓ×w×h

Cube Volume

V=s3

Cylinder Volume

V=πr^2h

Sphere Volume

V=4/3πr³

Cone Volume

V=1/3πr²h

Pyramid (Square/Rectangular Base) Volume

V=1/3(Area of Base)×h / Square base V=1/3s^2h

Triangular Prism (Occasionally Tested)

V=(1/2×base×height of triangle)×length of the prism

Force needed

weight of load / number of ropes

Volume of a rectangular solid or box

L x W x H

Perimeter of Rectangle

2 (L) + 2 (W)