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

Рассмотрим муху в движении. Чтобы определить его положение в трехмерном пространстве, используется декартова система координат, а единичные векторы вдоль оси задают его направление.
Векторная стрелка, которая тянется от начала координат к местоположению объекта, является вектором положения. Его можно представить в терминах единичных векторов.
Вектор положения представляет собой сумму компонент вектора на каждой оси, и их величины обеспечивают положение вдоль каждой оси.
Если муха продолжает движение, вектор ее положения изменяется, а разность векторов между векторами положения называется вектором смещения, Δr, который представляет собой изменение положения.
Например, если муха находится в точке А, а через время t достигает точки В, то с помощью векторов положения А и В можно получить вектор смещения мухи за время t.

Векторы положения и смещения

Чтобы описать движение объекта, первым делом следует описать его положение (где он находится в определённый момент времени). Более точно положение должно быть указано относительно удобной системы отсчёта. Система отсчёта — это произвольный набор осей, относительно которых описывается положение и движение объекта. Земля часто используется в качестве системы отсчёта для описания положения объекта относительно неподвижных объектов на Земле.

Кроме того, несколько важных видов движения происходит только в двух измерениях - то есть в плоскости. Эти движения могут быть описаны двумя компонентами положения, скорости и ускорения. Если объект движется относительно системы отсчёта, то его положение меняется; это изменение положения называется перемещением. Слово "перемещение" подразумевает, что объект переместился или был перемещен. Поскольку перемещение указывает направление, оно является вектором и может быть как положительным, так и отрицательным, в зависимости от выбора направления. Кроме того, анализ движения может содержать несколько векторов перемещения, а в физике может возникнуть множество применений с использованием цепочки перемещений. Таким образом, общее перемещение является суммой отдельных перемещений, которые следует тщательно вычислять, используя векторное сложение.

Этот текст адаптирован из <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>

Чтобы описать движение объекта, сначала нужно иметь возможность описать его положение (где он находится в любой конкретный момент времени). Точнее, позиция...

Education

JoVE Core

Mechanical Engineering

Машиностроение

Unit 1

Раздел 1

Physics Basics

Основы физики

KEY TERMS AND CONCEPTS

ОСНОВНЫЕ ТЕРМИНЫ И ПОНЯТИЯ

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 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

Using Vectors to Describe Motion

Description

Transcript