The so called circle in physics

This epiphany is more abstract, a bit of Zen flavor, hehe, what your teacher means is that you think physics is very interesting when you start learning, and you also think it is very interesting when you finish it. Just like when you first come into contact with something, you don't know what you will learn, but at that time your state of mind is fearless, just like a newborn calf is not afraid of tigers, once you touch a stone, you will be worried, disappointed, and may also have a psychological shadow, and eventually become very difficult. As the words say, the process is hard and the result is sweet.

From my experience in learning physics, some knowledge of physics is related to life, and it is helpful to pay attention to the causes and effects of some physical phenomena in life, which is helpful to improve the interest in physics learning. Relax your mood more and set yourself a goal: basic physics knowledge should be mastered, moderately representative problems should be accumulated and studied thoroughly, difficult questions can focus on his whole idea, after all, the exam is also based on intermediate and low-level knowledge, so that the grades are passable, the psychological pressure is small, and the room for improvement will be expanded.

When I was studying physics, I had this feeling: every time I learned a theorem, I had to analyze it as clearly as possible; When all these theorems of separation are clear, you will suddenly find that they are unified at a certain level, but they are a special case of a more general theory in different situations. For example, after learning about conservation of energy, you will find that the conservation of mechanical energy is just a special case of it.

Kepler's law is a corollary of Newton's three laws. Newtonian mechanics is a special case of the theory of relativity at low velocities. Wait a minute.

In fact, after learning it, you will feel that physics is simple, and the whole physics and even the entire universe can be summarized by the simplest formulas. Of course, this is just a feeling, and theoretical physicists are working in this direction. Let's look forward to it.

For beginners, I recommend getting the basic concepts straight. The difficulty in physics is the concept, and you don't have to do many questions, but it is better to have a more explanatory reference book to help you understand those basic concepts, basic theorems, including the connotation and extension of theorems.

I have the so-called enlightenment that you said, to put it bluntly, what is physics, the principle of all things. Physics is a kind of thought, using rational thinking to discover problems, think about problems, so as to understand a truth, that is, physics. Learning physics is very simple, it is to look around a lot, think with your brain, and be sure to think deeply until you figure it out.

I didn't. Study hard, do more questions, it will always be effective, whether it is an epiphany or gradual, it all depends on employment. Epiphany is also a thick accumulation, not a pie in the sky.

Other people's feelings are always someone else's, so why not experience them for yourself?

You take the physics book from beginning to end, from end to end, and write it down, OK, successful.

I did the exercises again.

The theorem in the circle is as follows:

1. The length of the tangent line theorem: if two circles have two outer tangent lines or two inner tangent lines, then the length of the two outer tangent lines is equal, and the length of the two inner tangent lines is also equal. If they intersect, then the intersection must be on the concentric line of the two circles.

2. Tangent length theorem: the length of the two tangent lines from the outer point of the circle to the circle is equal, and the point and the line at the center of the circle bisect the angle of the tangent line.

3. Cutting line theorem: a tangent line of a circle intersects with a secant line at point P, the tangent line intersects at point C, and the secant line intersects at two points A and B, then there is PC = Pa·Pb.

4. Circumferential angle theorem: The circumferential angle of an arc is equal to half of the central angle of the circle it opposes.

Corollary 1: The circumferential angles of the same or equal arcs are equal; In the same circle or equal circle, the arcs opposite the circumferential angles of the same circle are also equal.

Corollary 2: The circumferential angle of the semicircle (or diameter of the annihilation) is a right angle; The chord to which the circumferential angle of 90° is aligned is the diameter.

Corollary 3: If the middle line on the side of the triangle is equal to half of this side, then the pure triangle is a right triangle.

What is called a circle:

Geometry says: A figure composed of all points whose distance from the plane to the fixed point is equal to the fixed length is called a circle. The fixed point is called the center of the circle, and the fixed length is called the radius.

The set says: The set of points whose distance to a fixed point is equal to a fixed length is called a circle. Finger empty.

A closed curve formed by rotating around a point at a distance of a certain length in a plane is called a circle.

A circle has an infinite number of axes of symmetry.

A circle is a conic curve that is obtained by a planar truncated cone parallel to the bottom surface of the cone.

The circle is prescribed as 360°, which is the ancient Babylonians who moved a position about every 4 minutes when observing the rising sun on the horizon, and 360 positions in 24 hours a day, so the inner angle of a circle was prescribed to be 360°. This ° represents the sun.

Related theorems. Tangent theorem.

the radius perpendicular to the tangent point; A straight line that passes through the outer end of the radius and is perpendicular to this radius is the tangent of the circle.

Tangent is determined by a straight line that passes through the outer end of the radius and is perpendicular to this radius as a tangent of a circle.

A circle is an important concept in geometry and refers to a figure on a plane in which all points on a plane are at an equal distance from a fixed point.

This fixed point is called the center of the circle, and the distance is called the radius. The circle is a simple and beautiful shape that can be found everywhere in our lives and in nature.

In mathematics, a circle is one of the basic figures of plane geometry. It can be uniquely determined by the center of a circle and its radius, with the symbol "o" for the center of the circle and the symbol "r" for the radius. A circle can be represented by a concise formula:

x- h) +y- k) = r, where (h,k) is the coordinate of the center of the circle and r is the length of the radius.

Circles have many applications in everyday life. For example, the dial of a clock, wheels, dinner plates, coins, etc., are all round. Rounded wheels and rollers reduce friction and make vehicles and machines easier to move.

In addition, circular designs are also used in many architectural and artistic works, giving people a beautiful enjoyment and visual pleasure.

Circles related to the concept

1. The center of the circle: The center point of the circle is called the center of the circle, which is usually represented by the symbol "o". All points are at equal distances from the center of the circle.

2. Radius: The distance from the center of the circle to any point on the circle is called the semi-disturbed path, which is represented by the symbol "R". The radius of the circle determines the size of the circle.

3. Diameter: The distance between two points on the circle that passes through the center of the circle is called the diameter. The diameter is equal to twice the radius, which is denoted by the symbol "d".

4. Arc: The arc between two points on a circle refers to the arc part that connects these two points. Arc length refers to the length of the arc and can be calculated from the angle and radius.

5. Circumference: The circumference of a circle is called circumference, also known as perimeter or perimeter. The length of the circumference is equal to the diameter of the circle multiplied by (pi).

6. Fan: The area enclosed by the arc composed of the center of the circle and the two points on the circle is called the fan. The area of the sector can be calculated from the arc length and radius.

7. String: The line segment between any two points on the circle is called a string. The diameter is a special type of string that passes through the center of the circle.

The concept of circles.

Circle, center, radius, chord, diameter, arc, semicircle, superior arc, inferior arc, chord centr, equal arc, equal circle, concentric circle, bow, bow height.

Explanation: 1) The diameter is the string, but the string is not necessarily the diameter, the diameter is the longest string in the circle.

2) A semicircle is an arc, but an arc is not necessarily a semicircle.

3) Equal arcs can only be arcs in the same circle or equal circles, and there is no equal arc without the condition of "same circle or equal circle".

4) The length of the equal arc must be equal, but the arc of equal length is not necessarily the same arc.

The positional relationship between points and circles.

Note: The position relationship between the point and the circle corresponds to the quantitative relationship between the distance from the point to the center of the circle and the size of the radius, that is, the quantity relationship can be determined by knowing the quantity position relationship; Knowing the quantity relationship can also determine the location relationship.

Angles related to circles.

Circular central corner, rounded outer corner.

Description: These two kinds of angles related to the circle can be contrasted from (1) the position of the vertices of the corner; (2) The position relationship between the two sides of the angle and the circle, and grasp them from both sides.

Addendum: If the vertex of the angle is in the circle, then such an angle is called the inner corner of the circle, and the central angle of the circle is a special inner corner of the circle that is pure and absent; If the vertices of an angle are outside the circle, and both sides of the corner intersect the same circle, then such an angle is called an outer corner of the circle.

The relevant properties of the circle.

1) Determination of the circle.

1. > center of the circle, determine the position of the circle, and the radius determines the size of the circle.

2> three points that are not on the same line determine a circle.

2) Symmetry of the circle.

1> The circle is axisymmetric figure, and any straight line passing through the center of the circle is its axis of symmetry.

2> The circle is a central symmetrical figure, and the center of the circle is its center of symmetry.

Description: There are countless axes of symmetry in a circle, and there is only one center of symmetry, and a circle can be rotated around the center of the circle at any angle, which can coincide with the original figure, that is, the circle also has rotation invariance.

3) Vertical diameter theorem.

If a straight line has any two of the properties of (1) passing through the circle of the paulownia, (2) perpendicular to the chord, (3) bisecting the chord, (4) bisecting the inferior arc (5) bisecting the chord, then the straight line has the remaining three properties, namely:

Perpendicular diameter theorem: (1) (2).

Corollary 1: (1)(3).

1) (4) (or (5)).

2) (3) (5) (or (4)).

2) (4) (5) is "the diameter of the bisector chord (not the diameter) perpendicular to the chord, and the two arcs opposite the bisecting chord" where the string must be a non-diameter string, and if the string is a diameter, then the two diameters are not necessarily perpendicular to each other.

Corollary 2: The arcs sandwiched by the two parallel chords of a circle are equal.

Description: When solving problems related to circles, there are the following commonly referenced auxiliary lines:

1) The radius of the end of the string and the center of the circle.

2) Make the chord centrosis.

3) Connect the midpoint of the center chord (when it meets the midpoint of the chord).

4) Connect the center of the circle and the midpoint of the arc (when the middle of the arc is used as a pin point).

According to the nature of Chi Kaitan's rotation, rotate AOB around the center of the circle O to A'ob'Obviously aob= a'ob', rays OA and OA'Coincident, ob and ob'coincides, while the radius of the same circle is equal, oa=oa'，ob=ob', thus dotting A with A'Coincident, b and b'Superposition.

Thus, the arc AB is the same as the arc A'b'Coincident, ab with a'b'Superposition. Namely.

Arc ab = arc a'b'，ab=a'b'。

then the above theorem is obtained.

The same can also be obtained:

In an identical circle or an equal circle, if the two arcs are equal, then the angles to which they are opposed are equal, the chords to which they are opposed, and the centroid distance to which they are opposites are also equal. Yard paulownia.

In the same circle or equal circle, if the two strings are equal, then the angles to which they are opposed are equal, the arcs to which they are opposed, and the distance to the center of the chords to which they are paired.

So, in the same circle or equal circle, one set of quantities in the two central angles, two arcs, and two strings is equal, and the other groups of quantities corresponding to them are also equal.

1 Vertical diameter theorem.

2 Theorem of Relations in the Circle.

3 Tangent property theorem.

4 Tangent Determination Theorem.

5 Three-point circle theorem.

6 Circumferential angle theorem.

The circumference is 2 vultures, and the area is equal to the square of the vultures.

The concentric line bisects the common chord.