# Formulas

• PYTHAGOREAN THEOREM
• Resultant squared = side A squared + side B squared
• R2 = A2 + B2
• LAW OF COSINE
• Resultant squared = side A squared + side B squared - side A x side B x adjacent angle

• R2 = A2 + B2 – ABCos
• COSINE
• Ax = A cos ( Cos = adjacent side/hypotenuse)
• SINE
• Ay = A sin (Sin = Opposite side/hypotenuse)
• TANGENT
• Tan = Ry / Rx
• VELOCITY
• Velocity = Distance / Time
• v = d/t

• ACCELERATION
• Acceleration = Velocity / Time
• a = v/t
• a = v2 – v1 / t

• VELOCITY W/CONSTANT ACCELERATION
• Final velocity = initial velocity + acceleration x time
• V2 = v1 + at
• FINAL POSITION (DISTANCE) W/CONSTANT ACCELERATION
• Final position = initial position + half of the final velocity + initial velocity x time
• D2 = d1 + ½ (v2 + v1)t
• Final position = initial position + initial velocity x time + half of acceleration x time

• D2 = d1 + v1t + ½ at
• FINAL VELOCITY W/CONSTANT ACCELERATION
• Final velocity = initial velocity squared +2 x acceleration x final distance – initial distance

• V22 = v12 + 2a(d2 – d1)
• NEWTON’S SECOND LAW
• Acceleration = net force / mass
• A = Fnet/m
• NEWTON’S SECOND LAW AS WEIGHT
• Weight force = mass x gravity of planet
• Fw = mg
• WEIGHT AND ACCELERATION
• Force = mass x acceleration + gravity of planet
• F = m(a + g)
• KINETIC FRICTION FORCE
• Friction force = the kinetic coefficient of friction x Net force
• Ff = µkFNet
• Example, Push force = kinetic coefficient of friction x mass x gravity
• Therefore, Fp = µk x m x g
• PERIOD OF A PENDULUM
• Time = 2 x pi square root of length / gravity of planet
• T = 2L/g
• CIRCULAR VELOCITY
• Velocity = 2 x pi x radius / time
• V = 2r/t
• CENTRIPETAL ACCELERATION
• Acceleration = 4 x pi squared x radius / time squared
• Ac = 42r/t2
• CENTRIPETAL ACCELERATION W/VELOCITY
• Ac = v2 / r
• FREQUENCY
• Frequency = 1 / time
• F = 1/t
• Acceleration
• a = V2 / r
• Kepler's 3rd Law
• (period of 1st planet / period of 2nd planet) squared = (radius of 1st planet / radius of 2nd planet) cubed

(TA / TB)2 = (rA / rB)3

• Law of Universal Gravitation
• Force = (force of gravitational attraction x mass of 1st planet x mass of 2nd planet) / distance squared.

F = GmAmB / d2

• Period of Planetary Motion
• Time squared = (4 x pie squared / force of gravitational attraction x mass) x radius cubed

T2 = (42 / Gm)r3

• Speed of an object in circular motion
• velocity = the square root of (force of gravitational attraction x mass of earth / radius)

V = (Gme / r)

• Period for a satellite circling the earth
• time = 2 x pie x the square root of (radius cubed / force of gravitational attraction x mass of earth)

T = 2(r3 / Gme)

• Momentum
• momentum = mass x velocity
• P = mv
• Impulse-Momentum Theorem
• Force x the change in time = final momentum - initial momentum

Ft = P2 – P1

• Conserved Momentum
• momemtum of final A + momentum of final B = momentum of initial A + momentum of initial B

PA2 + PB2 = PA1 + PB1