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

ベクトル量は、大きさと方向の両方を持つ物理量です。
大きさは量のサイズまたは量であり、方向は空間内の向きです。
たとえば、ドアを開けるには、特定の方向に一定量の力が加えられます。したがって、力はベクトル量です。
物体の重量、つまり重力によって物体に加えられる力は、ベクトル量です。
ベクトルは、太字の斜体で表され、その上に矢印が表示されます。大きさは、垂直バーの間に同じベクトル記号で示すか、斜体の文字を使用して示されます。
幾何学的には、ベクトルは、方向を指す矢印と大きさを示す長さの線を使用して示されます。
点AからBへのオブジェクトの変位は、AからBで終わる矢印で示され、ベクトルはベクトルD、ABとして示されます。

2 つのベクトルは、大きさと方向が同じ場合、等しくなります。
ベクトルの負は、ベクトルの方向を逆にすることによって得られます。
2 つのベクトルが同じ方向を指している場合、それらは平行です。それらが反対方向を指している場合、それらは反平行です。

ベクトルの紹介

物理量の中には、大きさだけでなく方向も指定しなければならないものがあります。たとえば、米国沿岸警備隊が救助任務のために船やヘリコプターを派遣する場合、救助チームは救難信号までの距離だけでなく、信号が来ている方向も知る必要があります。 できるだけ早く現場に到着するためです。単位数（大きさ）と方向で完全に指定される物理量をベクトル量と呼びます。 ベクトル量の例には、変位、速度、位置、力、トルクが含まれます。 数学の言語では、物理ベクトル量はベクトルと呼ばれる数学的物体によって表されます。 ベクトル量は、その上に矢印が付いた斜体文字で表されます。 大きさのみを持ち方向を持たない量はスカラー量です。したがって、重量はベクトル量ですが、質量はスカラー量です。 同様に、速さはスカラー量ですが、速度はベクトル量です。

キャンプ旅行中の友人に、テントから 6 km 離れたところに素晴らしい釣り堀を発見したと話したとします。 キャンプ場からどの方向にあるのかを伝えなければ、友人はその釣り堀を簡単に見つけることができないでしょう。たとえば、「テントから北東に約 6 km 歩いてください」と言うかもしれません。ここで重要な概念は、距離の大きさ (6 km) と方向 (北東)という 2 つの情報を提供する必要があるということです。 この例では、テントから釣り堀へのような位置の変化は、変位として知られています。 これはベクトル量の例です。 幾何学的には、ベクトルは矢印として表されます。 それらの長さ (正の数) が大きさを示し、ベクトルを表すシンボルの周囲に絶対値表記を配置することによって示されます。 矢印は方向を示し、矢印の先端はベクトルの終点を示します。

2 つのベクトルは、大きさと方向が同じである場合に限り、等しくなります。 同じ方向を持つ 2 つのベクトルは平行ベクトルであると言われます。つまり、それらは互いに平行です。 ただし、ベクトルが反対方向 (正確に 180°) を向いている場合は、 最初のベクトルに対して、それらは逆平行であると言われます。 互いに垂直な方向を持つ 2 つのベクトルは、直交ベクトルと言われます。

このテキストは <a href="https://openstax.org/books/university-physics-volume-1/pages/2-1-scalars-and-vectors">Openstax, University Physics Volume 1, Section 2.1: Scalars and Vectors.</a> から編集されたものです。

一部の物理量を定義するには、大きさと方向の両方を指定する必要があります。たとえば、米国沿岸警備隊が派遣すると...

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Physics Basics

物理学の基礎

KEY TERMS AND CONCEPTS

主要用語と概念

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 機械工学は、平衡、力、トラス解析、構造力学などの重要なトピックをカバーする簡潔でわかりやすいアニメーション ビデオを提供します。実際のアプリケーションを探索し、科学者主導の実験を通じてこれらのコンセプトが実際に動作しているのを目撃してください。

mechanical engineering

Vectors in Motion and Direction

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Transcript