Name: vectors in motion and direction
Uploaded: 2023-09-22T11:49:38.000Z
Duration: 1 min 21 s
Channel: JoVE

벡터 수량은 크기와 방향을 모두 갖는 물리량입니다.
크기는 수량의 크기 또는 양이고 방향은 공간에서의 방향입니다.
예를 들어, 문을 열려면 특정 방향으로 일정량의 힘이 가해집니다. 따라서 힘은 벡터 양입니다.
중력으로 인해 물체에 가해지는 힘인 모든 물체의 무게는 벡터의 양입니다.
벡터는 굵은 이탤릭체로 표시된 문자로 표시되며 그 위에 화살표가 표시됩니다. 크기는 수직 막대 사이에 동일한 벡터 기호로 표시되거나 기울임꼴로 표시됩니다.
기하학적으로, 벡터는 방향을 가리키는 화살표가 있는 선을 사용하여 표시되고 길이를 나타내는 길이는 벡터의 크기를 나타냅니다.
점 A에서 B로 물체의 변위는 A에서 시작하여 B에서 끝나는 화살표로 표시되며 벡터는 벡터 DAB로 표시됩니다.

두 벡터는 크기와 방향이 같으면 같습니다.
벡터의 음수는 방향을 반대로 하여 얻습니다.
두 벡터가 같은 방향을 가리키면 평행합니다. 반대 방향을 가리키면 반평행입니다.

벡터 소개

일부 물리량을 정의하려면 크기와 방향을 모두 지정해야 합니다. 예를 들어, 미국 해안경비대가 구조 임무를 위해 선박이나 헬리콥터를 파견할 때 구조대는 조난 신호까지의 거리뿐만 아니라 신호가 오는 방향도 알아야 합니다. 가능한 한 빨리 그것에. 단위 수(크기)와 방향으로 완전히 지정된 물리량을 벡터량이라고 합니다. 벡터량의 예로는 변위, 속도, 위치, 힘, 토크 등이 있습니다. 수학 언어에서 물리적 벡터량은 벡터라고 불리는 수학적 객체로 표현됩니다. 벡터량은 위에 화살표가 있는 이탤릭체로 표시됩니다. 크기만 있고 방향이 없는 양은 스칼라 양입니다. 따라서 무게는 벡터 양인 반면 질량은 스칼라 양입니다. 마찬가지로 속도는 스칼라 양인 반면 속도는 벡터 양입니다.

캠핑 여행 중 친구에게 텐트에서 6km 떨어진 곳에 멋진 낚시터를 발견했다고 말했다고 가정해 보겠습니다. 캠프장에서 구멍을 찾을 수 있는 방향을 알려주지 않으면 친구가 구멍을 쉽게 찾을 수 없을 것입니다. 예를 들어 '내 텐트에서 북동쪽으로 6km 정도 걸어가세요'라고 말할 수 있습니다. 여기서 핵심 개념은 두 가지 정보, 즉 거리 또는 크기(6km)를 제공해야 한다는 것입니다. ) 및 방향(북동쪽)입니다. 이 예에서는 텐트에서 낚시 구멍으로의 위치 변화를 변위라고 합니다. 이것은 벡터량의 예입니다. 기하학적으로 벡터는 화살표로 표시됩니다. 길이(양수)는 벡터를 나타내는 기호 주위에 절대값 표기법을 배치하여 표시되는 크기를 제공합니다. 화살표 점은 방향을 나타내고, 화살촉은 벡터의 끝점을 나타냅니다.

두 벡터는 동일한 크기와 동일한 방향을 갖는 경우에만 동일합니다. 동일한 방향을 가진 두 벡터를 평행 벡터라고 합니다. 이는 서로 평행하다는 의미입니다. 그러나 벡터가 반대 방향, 즉 정확히 180° 첫 번째 벡터에 대해서는 역평행(antiparallel)이라고 합니다. 서로 직교하는 방향을 가진 두 벡터를 직교 벡터라고 합니다.

이 텍스트는 <a .="" href="https://openstax.org/books/university-physics-volume-1/pages/2-1-scalars-and-Vectors">Openstax, 대학 물리학 1권, 섹션 2.1: 스칼라 및 벡터.</a>

일부 물리량을 정의하려면 크기와 방향을 모두 지정해야 합니다. 예를 들어, 미국 해안 경비대가 파견 할 때 ...

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Physics Basics

물리학 기초

KEY TERMS AND CONCEPTS

주요 용어 및 개념

Introduction to Vectors

vectors in motion and direction

Vectors describe quantities that have both size and direction. They are used in physics to show how motion, force, and other quantities act in space.

A vector can be represented with an arrow. The length of the arrow shows the size, and the arrowhead shows the direction. This makes vectors useful for comparing how one quantity points relative to another.

Scalars are different because they have size only and no direction. Understanding the difference between vectors and scalars is an important first step in physics. It helps students read motion and force problems more clearly.

Vectors in Motion and Direction

introduction to scalers

Scalar Quantities in Physics

Scalar quantities in physics have size only. They do not include direction. This makes them different from vector quantities. Common scalar examples include mass, temperature, time, and energy. Each one can be described with a number and a unit. Because direction is not part of the value, scalars are often easier to compare and measure.

vector or cross product

Cross Product of Two Vectors

The cross product of two vectors gives a new vector that is related to both original vectors. It is also called the vector product. In many physics problems, this operation helps describe quantities that depend on direction as well as size. The result of a cross product has a direction set by the two input vectors. It is not the same as ordinary multiplication. The transcript focuses on the vector or cross product as a core vector operation students use when working with vectors in science.

introduction to vectors

Vectors describe quantities that have both size and direction. They are used in physics to show how motion, force, and other quantities act in space. A vector can be represented with an arrow. The length of the arrow shows the size, and the arrowhead shows the direction. This makes vectors useful for comparing how one quantity points relative to another. Scalars are different because they have size only and no direction. Understanding the difference between vectors and scalars is an important...

units and standards of measurement

Measurement Units, Standards, and SI Basics

Measurement units, standards, and SI basics help scientists describe physical quantities clearly. A unit gives a number meaning, while a standard provides a fixed reference for that measurement. Together, they make results easier to compare and understand. The International System of Units, or SI, is the most common measurement system in science. It uses agreed-upon base units for common quantities. These standards reduce confusion when measurements are shared across labs, classrooms, and...

accuracy and precision

Measurement Errors, Accuracy, and Precision

Measurement errors can affect how close a result is to the true value and how consistent repeated results are. Accuracy describes how close a measurement is to the accepted or true value. Precision describes how close repeated measurements are to one another. A result can be accurate, precise, both, or neither. A set of measurements may cluster tightly together and still be far from the true value. Another set may include values spread out from one another, even if one of them is close to the...

rules of significant figures

Counting Significant Figures in Measurements

Significant figures help students record measurements with the correct level of precision. They show which digits in a number are meaningful and which only help place the decimal point. In science class, this idea matters when writing and comparing measured values. The rules for significant figures explain how to count these digits in different numbers. Some digits are always counted, while others depend on where they appear in the number. Learning the rules makes it easier to report answers...

random and systematic errors

Measuring Error in Scientific Data

Random and systematic errors affect scientific measurements. Random errors cause values to spread around the true value. They make repeated measurements less consistent. Systematic errors shift measurements in the same direction each time. Understanding both kinds of error helps students judge data quality. Random error can come from small changes during measurement. Systematic error can come from a biased tool or method. Scientists look for these patterns so they can improve results and...

position and displacement

Tracking Motion with Position and Displacement

Position and displacement are key ideas in straight-line motion. Position tells where an object is located compared with a chosen starting point, called the origin. Displacement describes how far and in what direction the object has moved from its starting position. These ideas help describe motion clearly. Position can change as an object moves. Displacement focuses on the change in position, not just the path taken. That makes it useful for comparing motion in a simple and precise way.

position and displacement vectors

Using Vectors to Describe Motion

Position and displacement vectors describe motion in physics. A position vector shows where an object is located relative to a chosen origin. A displacement vector shows how far and in what direction the object moves from one point to another. These vectors are useful because they give a clear way to track movement in space. The video connects position and displacement to the idea of a reference point and shows how direction matters as much as distance. That makes them important for describing...

mass and weight

How Mass Differs from Weight

Mass and weight are related, but they are not the same. Mass is the amount of matter in an object. Weight is the force of gravity acting on that object. This difference matters because mass stays the same even when gravity changes. Weight can change if the gravitational pull changes. A person or object therefore has the same mass, but not always the same weight. The terms are often used in everyday speech as if they mean the same thing. In physics, they describe two different ideas.

acceleration due to gravity on earth

Free-Fall Acceleration on Earth

Free-fall acceleration on Earth describes how fast an object speeds up when gravity is the only force acting on it. Near Earth’s surface, this acceleration is nearly constant for many everyday situations. Gravity pulls objects toward Earth and gives them downward acceleration. This motion is often written as g, and it helps explain why falling objects gain speed as they move downward. The value of g is commonly used in physics to predict the motion of objects dropped or released near the...

tension

Tension in Ropes and Strings

Tension is the pulling force carried by a rope, string, or cable when it is stretched by a load. In physics, this force acts along the length of the object and pulls away from the objects at each end. A stretched rope can support a hanging mass because the tension in the rope balances the weight of the load. The same idea appears in many everyday situations, such as a cable holding a sign or a string lifting an object. Understanding tension helps students connect force diagrams to real motion.

gravitational force

How Gravity Acts Between Objects

Gravity is a force that pulls objects toward one another. On Earth, this force gives objects weight and keeps people, water, and other materials from drifting away. It also helps explain why planets and moons stay in motion around larger bodies. The strength of gravitational force depends on the masses of the objects involved. Larger masses create a stronger pull, while smaller masses create a weaker one. The distance between objects also matters, because gravity becomes weaker as objects move...

key terms and concepts

Learn how vectors show size and direction, how arrow length and arrowhead represent them, and how vectors differ from scalars in physics.

Vectors in Motion and Direction | JoVE K12

JoVE Core Mechanical Engineering offers concise, easy-to-understand animated videos covering key topics such as equilibrium, forces, truss analysis, and structural mechanics. Explore their real-world applications, and witness these concepts in action through scientist-led experiments.

mechanical engineering

Vectors in Motion and Direction

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Transcript