- •Donetsk - 2006
- •Донецьк - 2006
- •Contents
- •What is theoretical mechanics?
- •Kinematics . Kinematics of a Particle. Text 1. Kinematics
- •Kinematics is the section of mechanics, which treats of the geometry of the motion of bodies without taking into account their inertia (mass) or the forces acting on them.
- •2) The verbs corresponding to the following nouns:
- •Text 2. Methods of describing motion of a particle . Path.
- •Part 1. Vector Method of Describing Motion
- •Part 3. Natural Method of Describing Motion
- •Velocity of a Particle.
- •Part 1 . Determination of the Velocity of a Particle when its Motion is described by the Vector Method.
- •Part 2. Determination of the Velocity of a Particle when its Motion is described by the Coordinate Method
- •Part 3. Determination of the Velocity of the Particle when its Motion is described by the Natural Method
- •Unit 4. Acceleration Vector of a Particle.
- •Part 1. Determination of the Acceleration of a Particle when its Motion is described by the Vector Method.
- •Part 2. Determination of the Acceleration of a Particle when its Motion is described by the Coordinate Method
- •Unit 5. Tangential and Normal Accelerations of a Particle.
- •Verbs: direct, introduce, draw, denote, move, sweep, take.
- •Unit 6. Translational Motion of a Rigid Body
- •Unit 7.
- •2) The verbs in the left column with the nouns in the right one.
- •Unit 8.
- •Velocities and Accelerations of the Points of a Rotating Body.
- •Unit 9.
- •Equations of Plane Motion. Resolution of Motion Into Translation and Rotation.
- •Unit 10. The Path and the Velocity of a Point of a Body.
- •Part 1. Determination of the Path of a Point of a Body
- •Part 2. Determination of the Velocity of a Point of a Body
- •Verbs : design, lead to, construct, consider, specify, move, determine, join, calculate, perform.
- •Unit 11.
- •Verbs: obtain, perform, belong, lie, erect, exist , lead.
- •Equation of Motion and Solution of Problems.
- •Part 1. The two problems of dynamics.
- •Part 2. Constrained and unconstrained motion.
- •Verbs: apply, act, account, find, determine, resort.
- •Part 3. Free-body diagram.
- •Unit 14. Work
- •Part 1. Work and kinetic energy.
- •Part 2. Work
- •Part 3. An example of the work done on a body by a variable force.
- •Unit 15. Kinetic energy. Power and Efficiency.
- •Part 1. Kinetic energy.
- •Equal, bring, avoid, do, result, call, correspond, lead, act.
- •Part 2. Power.
- •Part 3. Efficiency.
- •As, due to, because, so that, on the other hand, in addition to , since.
- •Commonly used mathematical symbols and expressions.
- •The Greek alphabet.
- •Vocabulary
- •Literature
As, due to, because, so that, on the other hand, in addition to , since.
a) We assume the machine operates uniformly.
b) There is no accumulation or depletion of energy within it.
a) Efficiency is always less than unity.
b) Every device operates with some loss of energy.
a) There is always some loss of energy in mechanical devices involving moving parts.
b) Kinetic friction forces do the negative work.
a) Mechanical friction results in energy loss.
b) There may also be electrical and thermal energy loss.
a) Efficiency is always less than unity.
b) Energy cannot be created within the machine.
a) Any motor, no matter how small, can deliver a large amount of energy if given sufficient time.
b) A large and powerful machine is required to deliver a large amount of energy in a short period of time.
a) The total work is not a measure of the capacity of a machine.
b) A motor of any size can deliver any amount of energy if given sufficient time.
Appendix 1.
Commonly used mathematical symbols and expressions.
+ |
plus; the sign of addition (знак сложения), positive |
- |
minus; the sign of subtraction (знак вычитания), negative |
± |
plus or minus/approximately |
× |
(is) multiplied by /times; multiplication sign |
÷ |
(is) divided by; division sign; ratio sign |
= |
is equal to /equals ; sign of equality |
≠ |
is not equal to / does not equal to |
< |
is less than |
≤ |
is less than or equal to |
> |
is more than / greater than |
≥ |
is more than /greater than or equal to |
% |
per cent |
log e |
natural logarithm or logarithm to the base e |
√ |
(square ) root |
3 √ |
cube root (out ) of |
n √ |
n-th root (out ) of |
x2 |
x [eks] squared |
x3 |
x [eks] cubed |
x4 |
x [eks] to the power four/ to the fourth power |
dy/dx |
derivative of y with respect to x |
d2y/dx2 |
second derivative of y with respect to x |
x |
absolute value of x |
|
the integral of |
f (x) dx |
the integral of a function of x over dx |
mn |
the integral between limits n and m |
[] |
brackets, square brackets |
() |
round brackets |
|
is parallel to |
┴ |
is perpendicular to |
∟ |
right angle |
‘ |
apostrophy |
, |
comma |
. |
full stop |
0 |
degree |
a ′ |
a prime |
a ″ |
a second prime or a double prime |
a ′″ |
a third prime or a triple prime |
b1 |
b sub one or b first |
b2 |
b sub two or b second |
lim |
limit |
sin |
sine |
cos |
cosine |
tan, tg |
tangent |
ctn,cot |
cotangent |
sec |
secant |
sin -1 |
antisine |
cos-1 |
anticosine |
f (x) or φ (x) |
function of x |
∆ x |
increment of x |
dx |
differential of x |
0.1 |
zero point one |
0.34 |
zero point three four |
0.001 |
zero point zero zero one |
⅛ |
one - eighth |
¼ |
one quarter |
½ |
one half |
⅓ |
one third |
¾ |
three-quarters |
3/462 |
three over four-six-two |
20/83 |
twenty over eighty-three |
π |
pi [pai] |
r |
[ α] – radius of circle |
π r2 |
pi r squared [pai α skweәd ] |
ε |
summation |
Appendix 2.