Name: using vectors to describe motion
Uploaded: 2023-09-22T11:49:39.000Z
Duration: 1 min
Channel: JoVE

動いているハエを考えてみましょう。その位置を 3 次元空間に配置するには、デカルト座標系が使用され、軸に沿った単位ベクトルがその方向を提供します。
原点からオブジェクトの位置まで伸びるベクトル矢印が位置ベクトルです。これは、単位ベクトルで表すことができます。
位置ベクトルは、各軸上のベクトル成分の合計であり、それらの大きさは各軸に沿った位置を提供します。
フライが動き続けると、その位置ベクトルが変化し、位置ベクトル間のベクトル差は変位ベクトルΔrと呼ばれ、位置の変化を表します。
たとえば、フライが点Aにあり、時間tの後に点Bに到達する場合、AとBの位置ベクトルを使用して、時間tのフライの変位ベクトルを取得できます。

位置ベクトルと変位ベクトル

物体の動きを説明するには、まずその位置 (特定の時点での位置) を説明できなければいけません。 より正確には、便利な座標系を基準にして位置を指定する必要があります。 座標系は、オブジェクトの位置と動作を記述するための任意の軸のセットです。 地球は、地球上の静止物体に対する物体の位置を記述するための基準枠としてよく使用されます。

さらに、いくつかの重要な種類の動きは 2 次元のみ、つまり平面内で発生します。 これらの動きは、位置、速度、加速度の 2 つの要素で説明できます。 オブジェクトが座標系に対して移動すると、オブジェクトの位置が変わります。 この位置の変化は変位と呼ばれます。 変位という言葉は、物体が移動した、または位置が変わったことを意味します。変位は方向を示すため、ベクトルであり、選んだ方向に応じて正または負になります。 また、運動の解析には多くの変位を組み込むことができ、物理学の多くのアプリケーションでは一連の変位を含めることができます。 したがって、総変位は個々の変位の合計となるため、ベクトル加算を使用して慎重に評価する必要があります。

このテキストは <a href="https://openstax.org/books/university-physics-volume-1/pages/4-1-displacement-and-velocity-vectors">Openstax, University Physics Volume 1, Section 4:1 Displacement and Velocity Vectors</a> から編集されたものです。

物体の動きを説明するには、まずその位置(特定の時間にどこにあるか)を説明できる必要があります。より正確には、位置...

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

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 motion in one, two, or three dimensions.

The lesson also shows how to represent these vectors using arrows and coordinate systems. By comparing the starting point and ending point, students can see the difference between an object’s location and its change in position. This helps build the foundation for later topics in kinematics.

Using Vectors to Describe Motion

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 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...

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

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 position vectors and displacement vectors describe an object’s location and movement in 1D, 2D, and 3D using arrows and coordinates.

Using Vectors to Describe Motion | 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

Using Vectors to Describe Motion

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