On the x'y coordinate plane, a circle with radius of one is called a unit circle.

Using an angle 0 made by the traxis and radius vector OP, the position of a moving point P on the circumference can be determined.

In short, the coordinates of the point P are determined by the value of 0, and the following Eqs. (1.1) result:

The cosine, sine, and tangent functions are called trigonometric (ones).

Let's consider the periodicity of the trigonometric functions.

The general angle of radius vectordose not change after n revolutions, where 0 = 0 + 2nn (n is an integer).

The function f(x + p) = f(x) is generally called a periodic function, and constant p is called a period.

The smallest p in the positive value is called specifically, a fundamental period:

Therefore. sin cos are periodic functions of fundamental period 2mt, and tan 0 is that of period n.

Binomial theorem being applied, the expression (1 + x)" can be expanded:

When the value x is particularly small, the terms of higher order of x can be neglected.

So, an approximate value might be obtained by the Eq. 2.2).

Now, let's try to check the approximation of the above equations.

The smaller the values of x and n are the more accurate Eq. 2. 2) will become.

In the international system of units, the base unit of length is the meter, Symbol m.

In October, 1983, the length of the one meter was defined as the distance traveled by light in vacuum during a time interval of 1/299792458 second.

Originally, one meter was intended to be one ten miloth of the mes dian quadrant: the dis trce from the North Pole to the equator.

(E) took six years of sulveys and the French Academy of Science constructed the standard meter bar made of platinum in 1799.

Afterwards the unchangeable values for temperature and other external conditions were separately considered to be standards.

This meter bar was recommended as the international prototype meter bar and the length of one meter was first defined in 1889.

One meter had been 1650763.73 times as long as (that) of the wavelength in vacuum of the orange colored spectral line of the 86 Kr atom in 1960.

Such quantities as length, mass, time, speed, and energy are examples of scalar quantities (which) have magnitude but no direction

In contra duch quant as displace et, veloaty ae eration, and of -are examples of vector quantities (which have direction as well as magnitude.

Therefore, a vector can be draw by a line whose length is proportional to the magnitude of the quantity and (whose) direction is that) of vector.

In vector addition, there are womethod parallelogram and triangle methods.

Draw the two vectors from a point and make a parallelogram by those vectors.

Then, the resultant 14 vector (A + B) is represented by the diagonal C of the parallelogram, as shown in Fig. 4(a).

If the two vectors S are represented by two sides of a triangle taken in order, the resultant vector is represented by the third side of the triangle. See Fig.4(b).

Speed and Veloct have oten been contused in ther use heause ther have the same dimension as length divided by time.

However, velocity is defined as a size of the motion, a vector quantity with direction and the spoed, but a calar quantior shows only the manitude of veloci

Next, lets in 10 consider an example （0相当） showing these differences.

When the object moves on a circular route at the uniform speed, the velocity is not fixed as the direction changes, even though the speed of the object is constant.

When the object moves on a straight line at a fixed speed, speed and velocity become equivalent and they are equal to each other numerically.

object at rest remains stationary and a moving (one) keeps uniform motion unless acted upon by some external forces.

object at rest remains stationary and a moving (one) keeps uniform motion unless acted upon by some external forces.

an object at rest or in uniform motion will remain at rest or in uniform liner forces are applied to it or when the external forces equilibrate.

This fact is called the law of inertia or the first law of motion.

A force often appears as an interaction between two forces.

The equal reaction of the magnitude (that) simultaneously has the opposite direction to (that) of the action V1 exists as shown in Fig.6.

This is called the laws of action and reaction or the third law of motion.

When a force acts on an object, an acceleration proportional to the magnitude of the force occurs in the direction of the force.

Generally, the magnitude of the acceleration is directly proportional to (that) of the force and is inversely proportional to the mass of the object.

With force F, acceleration a, and mass m of the object, the relation of F = ma is obtained.

this isthe when multiple forces affect the object.

It is possible, in principle, to analyze the motion of the object by solving this equation given the size of the force acting on the object.

Mass m is the quantity peculiar to the object and （it） means the magnitude of the inertia for the object.

When the force is fixed, the bigger the mass of the object, the smaller the acceleration will be.

The rotion in （which） the obiect moves alons the cireumference of a cirele is called aircular motion； and the motion (that) rotates at fixed speed is called uniform circular motion.

Let's try to consider the case in (which) (it) rotates from point A to A' in uniform circular motion on the circumference of the circle center ana radius r shown in Fig.8.

The proportion of the angle in (which) radius vector OA changes for one second is called angular velocity wi S is defined as rotation angle @ divided by elapsed time t in the following equation:

The angular velocity a is fixed in uniform circular motion.

Then, the time in (which) the object rotate the circumference is called period

So we have the following equation between period T and angular velocity w:

The number of rotations of the object in one second is called the number of revolutions n.

There is also the relation between the number of revolutions n and angular velocity w:

The period I and the number of revolutions 2 / 1c -2 are reciprocal numbers to each other by Eq. (8.2) and Eq.

The capacity for doing work is generally called the energy, and the unit is L.

Mecanical energy can be classified into potential energy and kinetic energy.

Let's try to consider the case (where the object of mass m moves at a speed of u with height h above the ground, as shown in Fig.9.

Potential energy Rof the obiect is P-man and kinetic energy K of that) is K= ½ mu

Then, though the energy changes its form in the closed system (where) the external force does not work, its total amount is preserved.

(This is called the law of the conservation of energy.

Bernoulli's law conversion of the form in mechanical energy and the first law of thermodynamics does between mechanical and thermal energy; both laws express a part of the law of the conservation of energy.

The capacity for doing work is generally called the energy, and the unit is L.

The auxiliary scale for reading smaller intervals of the main scale, thus measuring a length and an angle precisely, is called a vernier.

The vernier dividing (n - 1) interval or (n + 1) interval on the main scale into n equal parts is used to read /n of the small intervals on (it).

For example, when the vernier dividing nine intervals of the main scale with minimum scale graduated one millimeter into ten equal intervals is used, the difference in a reading of main scale and a vernier scale, namely measurement accuracy, is shown in the following equation:

To read a vernier, add the reading in tenths of a millimeter indicated by the graduation on the auxlliary (that) agrees with the longitudinal line on the main scale to the one in millimeters seen on the main scale.

Also vernier caliper anc micrometer are measuring machines for length using the vernier principle.

A micrometer is a precise length measuring instrument to (which the principle of the screw is applied, and an outside micrometer is the most generally known.

The pitch of the spindle screw in the micrometer is 0.5mm.

By one revolution of the thimble, the spindle goes in or out, away from or towards, the anvil 0.5 mm.

The vertical lines on the sleeve are graduated from O to 25 mm at intervals of 0.5 mm.

Therefore, turning the thimble twice, the spindle goes in or out accurately for 1mm.

The part (where) the thimble slopes is divided into 50 equals parts, and the number from 0 to 50 is read at every fifth of the scale mark.

Because one revolution of the thimble makes the spindle accurately travel 0.5 mm in or out, one scale of the thimble will correspond to 1/50 of 0.5 mm, namely 0.01 mm.

In the actual moasureent ada the readine in 1100m units on the intle which aeres with thevertcalline on the sleeve, and the (one) in mm shown on the sleeve.

When a value of 23.4 mm is obtained in the measurement of a length, i means that the length is under 20.45 mm and over 23.35 mm. For the value of 23.40 mm,

it is similarly under 23.405 mm and over 23.395 mam. The mathematical meanings o/23. 4 and 23.40 a the same.

However, 22.400 measure more precisely than 23.4 and the meaning is completely different.

The number with the meanings in the measured value is the significant figure.

The significant figure is three figures in the case of 0.0123 m length， but the significant figure may be interpreted as five figures when this number is expressed with 12300um

In any calalata basea a the eastied e the ent euree ust be suficiently considered

this is a mathod Bor proeath Orpotmona at

Its main purpose is to decide the constants in an empirica equation (which) give the best fit for a series of data.

Ihe set of data could be expressed in a straight line as long as they have no error, but this is not always so.

Making the sum of the residual square to each constant minimum, we could obtain the closest fitting constants a anc 1 b.

Though it is troublesome to handle, the result can express a series of data more correctly.

sinon ahi tallpre ti in tegarmd an e lninia af ano ayannn? on fine indine gon be written as in Eq. (14.1).

where in is said to be the logarithm of y to the base x.

Generally, logarithms can be classified into two types; (1) common logarithms are to the base 10, written 1og1o y or logy: 2) natural logarithms to the base e = 2.71818.., logey or iny.

Namely, when y= x' is potted on a chart with togariRie sales on both ares, the result is a straieht line of slope n as shown in Fig. 14.

Many lans in natural scent are dekermme rega diess of the method of eletig the fundamental unit as a physical quantity.

That is to say, it is a necessary condition that both sides of a mathematical expression IS S1 (rie har the ar , m ea inensin on th hae ari

The nghed tati he for of the law to a certain extent using this property is called dimensional analysis.

For example, the following equation is assumed since period til of spring pendulum is related to mass m[kg] of the pendulum and spring constant k[N/m = kg/s°]:

The relation of 1 = -2b and b = -c is obtained from [T] and [M], since the value of the index in both corresponding sides must be equal.

However, the decision is not possible tor if this method.

A sealed container filled with stationary fluid (which) does not contract is considered.