Mechanics

Front 1

resultant of concurrent forces,

R x = summation of forces of x.

R y = summation forces of forces y.

Resultant = squareroot of Rx squared + Ry squared.

tangent theta = Ry over Rx

law of sines,

a over sine alpha = b over sin beta = c sin gamma.

law of cosines:

c squared = a squared + b squared minus 2 ab cosine gamma,

b squared = a squared + c squared minus 2 ac cosine beta,

c squared = b squared + c squared minus 2 bc cosine alpha.

Back 1

friction:

friction force = mhew (u) n.

mhew (u), or coefficient of friction = tan phi.

phi, or angle of friction = arc tangent mhew (u)

belt friction:

T2 over T1 = e raised to mhew beta.

beta, is in angle in radian.

Front 2

dynamics - kinematics

velocity = S, or distance over time.

acceleraion = velocity over time.

uniform rectlinear motion:

S, or distance = S. o., or initial distance plus Velocity ,time.

uniformly accelerated rectilinear motion.

V, or velocity = V. O. plus a, t.

S, or distance = S. o. plus V. o., t plus 1/2 a. t squared.

V squared = V. o. squared plus 2 a, Times S minus So.

Back 2

curvilinear motion:

x= V.o.x times t.

y = V. o. y. times t minus 1/2 g t squared.

Vy = V. o.y. minus g.,t.

Vy squared = V.o.y. squared minus 2 gy.

Front 3

rotation of elements:

theta , or angular displacement, (in radians) = w.,t.,

w is angular speed, in rad per second.

constant acceleration:

w = w.o. plus apha, t.

alpha is equal to angular acceleration., rad per second squared.

theta, = w.o., t plus 1/2 aplaha, t squared.

w squared = w.o. squared plus 2 apla S.

Back 3

translation and rotation:

S = r, theta.

a = r, aplha.

V = r, w.

dynamics:

F = m.,a.

ideal angle of banking:

tangent theta = V squared over g,. r.

where , V is the rated speed in m per second.

R, is the radius of the curve in meter.

and g is the acceleration due to gravity.,9.81meter per second squared.

or, tangent, (theta plus phi) = V, squared over, g. r.,

where phi is the angle of friction, = arctangent mhew (u).

if the car is slipping down.,

tangent (theta minus phi) = v squared over g,.r.

Front 4

work and energy:

U (work) = (F cos aplha) times S., where ,s is the displacement.

kinetic energy, T = 1/2 m ,V squared.

impulse and momentum:

impulse = Force times time.

momentum = m,V or , W., V., over g.

law of conservetion of momentum.,

m1v1 + m2 v2 = m1 V1,prime plus m2 V 2 prime.

coeficient of restitution.:

E , v1 minus v2 = (v2 prime minus v1 prime).

Back 4

radius of gyration of an area.

r.x. = squareroot of I.x over A.

r.y. = squareroot of I.y. over A.