- •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
Verbs: direct, introduce, draw, denote, move, sweep, take.
Particles : between, in, along, into, around, through.
We should … .axis Mτ'…… point M1.
It is necessary to …..account that .
The tangent M …… the binormal Mb with an angular velocity .
These particles ……..different planes.
We need to ……..this quantity ……this equation.
The component is always …….. the inward normal.
Let us ……..the angle …..these vectors.
Ex.7. Use the correct form of the word in brackets.
We have proved that the ……. (project) of the …… (accelerate) of a particle on the tangent to the path is equal to the first ……. (derive) of the ….. (number) value of the velocity, or the second ……. (derive) of the ……(place) S, with respect to time.
The …… (accelerate) vector is the diagonal of a parallelogram ……(construct) with the components and as its sides. These components are ….. (mutual) perpendicular.
The ……(tangent) component of the …… (accelerate) is equal to the rate of change of the speed of the particle, while the …….(norm) component is equal to the square of the speed …….(divide) by the radius of ……..(curve) of the path at point P.
Ex.8. Join two simple sentences into one complex with the help of the following words making some changes if necessary :
When, while, if, since, as, hence.
a) The acceleration of a particle lies in the osculating plane.
b) The projection of this vector on the binormal is zero.
a) Particle M is moving in one plane.
b) The tangent M sweeps around the binormal Mb with certain angular velocity.
a) We introduce the meaning of the velocity into the equation.
b) We can obtain one more equation for calculating the acceleration that is frequently used in practice.
a) The component is always directed along the inward normal.
b) wn is always more than 0.
a) The component is directed along the inward normal.
b) The component can be directed either in the positive or in the negative direction of axis M.
a) These components are mutually perpendicular.
b) The magnitude of vector and its angle to the normal Mn are given by the following equations
a) The path and the equations of motion are known.
b) We can determine the magnitude and direction of the velocity and acceleration vectors of the particle for any instant.
Ex.9. Find the synonyms in Part 1 to the words in Part 2.
|
Part 1. |
|
Part 2. |
1 |
increase of velocity |
a |
velocity |
2 |
alteration |
b |
component |
3 |
speed |
c |
increase |
4 |
element |
d |
decrease |
5 |
movement |
e |
quantity |
6 |
constituent |
f |
acceleration |
7 |
go up |
g |
particle |
8 |
inside |
h |
motion |
9 |
reduce |
i |
change |
10 |
measure |
j |
center |
Ex.10. Find the antonyms in Part 1 to the words in Part 2.
|
Part 1. |
|
Part 2. |
1 |
indefiniteness |
a |
stationary |
2 |
directly proportional |
b |
together |
3 |
never |
c |
construct |
4 |
separately |
d |
limit |
5 |
different |
e |
inverse |
6 |
destroy |
f |
equal |
7 |
moving |
g |
always |
Ex.11. Translate into English.
Надо найти проекцию этого вектора на оси координат.
Это уравнение может быть составлено с учетом проекций вектора на другие оси координат.
Теорема проекций вектора на оси координат применяется при естественном методе описания движения.
Необходимо преобразовать правую часть уравнения.
Если числитель и знаменатель дроби умножить или разделить на одно и тоже число, то значение дроби не изменится.