Name: why motion seems different in accelerating frames
Uploaded: 2023-04-30T10:54:29.000Z
Duration: 1 min 27 s
Channel: JoVE

K12 Standards

Pennsylvania State Academic Standards

9-12

Physical Science

Forces and Interactions

3.2.9-12.J

Non-inertial Frames of Reference

ニュートンの法則が成り立つ基準系は、慣性系として知られていることを思い出してください。ただし、ニュートンの法則に反する参照系があり、非慣性参照系と呼ばれます。
非慣性系は、慣性系に対して加速または減速しています。
たとえば、飛行機が離陸するとき、乗客は飛行機の加速とは逆の後方の力を感じます。これは、物体が正味の外力の方向に加速されるニュートンの第二法則に違反しています。
非慣性系では、物体の動きを説明するために、物理的な起源を持たない慣性力または架空の力が必要です。したがって、力学では、慣性フレームを使用する方が便利です。
理想的には、地球に固定された基準系は、その公転と自転のために非慣性です。ただし、地球の自転による力は、小さな機械的な動きでは無視できますが、風のパターンのような大規模な動きに影響を与えます。
このフレームの架空の力は、北半球では時計回りに、南半球では反時計回りに風をそらします。

利益相反は宣言されていません。

非慣性座標系

慣性系に対して加速または減速する基準系は非慣性系です。 これを理解するために、飛行機の離陸、車の角を曲がる、メリーゴーランドに乗る、熱帯低気圧の円運動に共通するものを考えてみましょう。 これらすべての系は、地球に対して加速、減速、または回転しています。 したがって、それらはすべて非慣性フレームです。 これらすべての系は慣性力を示しますが、観察者の基準系が加速または回転しているため、単に動きから生じているように見えます。 使用されている参照フレームを調べることで、これらの観点を調整できます。 物理学者は、分析する状況に最も便利な基準座標系を選択します。 物理学者は、都合がよければ、いつものように慣性力やニュートンの第二法則を問題なく含めることができます。 同様に、非慣性 (加速) 座標系が役立つ場合には使用されます。 たとえば、光速に近い速度で移動する宇宙船内の宇宙飛行士の動きを議論する場合、これは特殊相対性理論に当てはまるため、さまざまな基準系を考慮する必要があります。

地球は、その回転によって生じる影響をほとんどまたはまったく心配することなく、慣性座標系として使用できます。 ただし、そのような影響は、たとえば気象系の回転などに存在します。 北極の上から見ると、地球は反時計回りに回転しており、地球の北半球での運動には右方向のコリオリ力がかかります。 南半球ではその逆が起こり、力は左側にあります。 地球の角速度が小さいため、コリオリの力は通常は無視できますが、風のパターンなどの大規模な動きに対しては大きな影響を与えます。 コリオリの力により、北半球のハリケーンは反時計回りに回転しますが、南半球の熱帯低気圧は時計回りに回転します。

熱帯低気圧の回転とメリーゴーランドのボールの軌道は、慣性とその下の系の回転によって同様に説明できます。 非慣性系を使用する場合、曲線経路を説明するにはコリオリの力などの慣性力を発明する必要があります。 これらの慣性力の物理的原因を特定できるものはありません。 慣性系を使用すると、慣性によって経路が説明され、あらゆる力の特定可能な発生源が存在します。 どちらを使用しても自然を説明できますが、すべての力には起源と説明があるため、慣性系でのビューの方が簡単です。

このテキストは <a href="https://openstax.org/books/university-physics-volume-1/pages/5-6-common-forces"> から編集されたものです。 Openstax, University Physics Volume 1, Section 5.6: Common Forces</a> および<a href="https://openstax.org/books/university-physics-volume -1/pages/6-3-centripetal-force"> Section 6.3: Centripetal Force.</a>

慣性系に対して加速または減速する参照系は、非慣性系です。これを理解するために、何で離陸するかを考えてみましょう...

Education

JoVE Core

Physics

物理学

Unit 1

ユニット1

Newton's Laws of Motion

ニュートンの運動の法則

KEY TERMS AND CONCEPTS

主要用語と概念

why motion seems different in accelerating frames

A non-inertial frame of reference is a frame that accelerates, decelerates, or rotates relative to an inertial frame. In these frames, motion can look unusual because the observer is moving with the system. That is why an airplane taking off, a car turning a corner, a merry-go-round, and a tropical cyclone can all be examples of non-inertial motion.

These situations can show inertial forces, which seem to appear because the frame itself is accelerating or rotating. The force does not come from a physical source in the usual sense. Instead, it is tied to the observer’s frame of reference.

Physicists choose the reference frame that is most useful for the problem being studied. They can use inertial frames and apply Newton’s second law in the usual way. They can also use non-inertial frames when that makes the description easier.

Different frames of reference matter in special cases, such as an astronaut in a spacecraft moving near the speed of light. This is important in the special theory of relativity. In many problems, the Earth is used as an inertial frame because its rotation causes little trouble.

Even so, Earth’s rotation does affect some motions. Viewed from above the North Pole, Earth rotates counterclockwise. Motion in the Northern Hemisphere then experiences a Coriolis force to the right, while the Southern Hemisphere experiences a force to the left.

Because Earth’s angular velocity is small, the Coriolis force is usually negligible. It still has major effects on large-scale motion, such as wind patterns. It helps explain why hurricanes in the Northern Hemisphere rotate counterclockwise and why tropical cyclones in the Southern Hemisphere rotate clockwise.

The path of a ball on a merry-go-round and the motion of a tropical cyclone can also be explained by inertia and by the rotation of the system underneath. When a non-inertial frame is used, inertial forces such as the Coriolis force must be added to explain the curved path. When an inertial frame is used, inertia explains the motion, and every force has a clear source. Both views can describe nature, but the inertial frame is usually simpler.

Why Motion Seems Different in Accelerating Frames

why-motion-seems-different-in-accelerating-frames

force

Understanding Force in Motion

Force is a push or pull that acts on an object. It has both magnitude and direction, so force is a vector quantity. In everyday life, force appears when we open a door, walk down a street, lift a fork, or touch a baby's face. Forces also shape matter at the smallest scales. The atoms in our bodies are held together by electrical forces. The nucleus of an atom is held together by nuclear force, which is the strongest force known to us. The study of motion is called kinematics. Kinematics...

types of forces

Contact and Field Forces in Physics

Forces in physics are often grouped as contact forces and field forces. Contact forces happen when objects touch directly. Field forces act without direct physical contact. They come from a field, which is a region of space that can be detected by the force it exerts on a body. Scientists describe four fundamental force fields in nature: gravitational, electromagnetic, strong nuclear, and weak nuclear. The gravitational field gives a body its weight. The electromagnetic field includes static...

newton's first law: introduction

Newton's First Law and Inertia

Newton's first law of motion explains inertia and how forces change motion. Motion can be striking to observe, from a dolphin jumping from water to a bird in flight or a satellite moving in orbit. The study of motion is kinematics, which describes velocity and acceleration. Dynamics goes further by examining the forces that affect moving objects and systems. Newton's laws of motion are the foundation of dynamics. They are simple in form, but they describe a wide range of natural behavior.

newton's first law: application

Newton's First Law and Friction

Newton's first law explains why friction changes an object's motion. It says that an object at rest stays at rest, and an object in motion keeps moving unless a net external force acts on it. A net external force is the overall force from outside the object that causes a change in velocity, meaning a change in speed or direction. This idea gives a cause-and-effect reason for motion, rather than just describing what we see. Galileo first developed the idea behind the first law of motion, and...

internal and external forces

External Forces and Motion Changes

External forces and motion changes are linked in Newton’s first law. A net external force causes a change in motion. External forces act on an object or system from outside that object or system. Internal forces come from inside the system of interest. They act on one part of an object and are exerted by another part of the same object. These forces do not cause acceleration when the whole system is studied. When analyzing motion, the internal forces are ignored. Instead, only the external...

newton's second law

Force, Mass, and Acceleration

Newton's second law connects net force, mass, and acceleration. It explains how an object's motion changes when external forces act on it. The law gives a clear cause-and-effect link that can be used to make calculations. All external forces on a system are added together to find the net force, or F net. A larger net external force produces a larger acceleration. The acceleration points in the same direction as the net force. Mass also affects the result. A larger mass means more inertia, so...

mass and weight

Weight Changes, Mass Stays Constant

Mass and weight are related, but they are not the same. In physics, weight is the pull of the Earth on an object. It depends on how far the object is from the center of the Earth. Mass is the amount of matter in an object, and it does not change with location. Everyday language can make this difference confusing. Medical records often list body weight in kilograms, even though the correct force unit is the newton. That can make mass and weight seem interchangeable. In physics, however, they...

weightlessness

Weightlessness in Free Fall

Weightlessness happens when contact forces disappear, even though gravity is still present. In physics, an object in free fall has only gravity acting on it. If the net external force on the object is its weight, the object is accelerating toward the center of the Earth. Galileo showed that, without air resistance, all objects fall with the same acceleration g. On Earth, falling objects are never truly in free fall because air always pushes upward with some resistance force. That is why real...

apparent weight

Scale Readings in Motion and Water

Scale readings can change when an object is moving or submerged in water. The force we call true weight is the gravitational force acting on an object. When motion or fluid forces are present, the reading can differ from that true weight. In water, this changed reading is called apparent weight, and it equals true weight minus the buoyant force. A bathroom scale in an elevator shows how this works. At rest, the scale reads the force the person pushes downward on it. The only forces on the...

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newton's third law: introduction

Newton's Third Law in Force Pairs

Newton's third law explains how force pairs work in motion and interactions. When one body exerts a force on a second body, the first body experiences a force that is equal in magnitude and opposite in direction. A simple example is a person pushing on a wall. The wall pushes back on the person with an equal and opposite force. This is why Newton's third law is often described as action and reaction, where the action is the force exerted and the reaction is the force experienced afterward. <br...

newton's third law: examples

Newton's Third Law in Motion

Newton's third law explains how forces come in pairs during motion. It says that every action has an equal and opposite reaction. In these examples, the two forces act on different systems, so they do not cancel each other out. A swimmer pushing off the side of a pool shows this clearly. The swimmer pushes against the wall with their feet and then accelerates in the opposite direction. The wall pushes back with an equal and opposite force. If the swimmer is the system of interest, the wall's...

drawing free-body diagrams: rules

Free-Body Diagrams for Newton’s Laws

Free-body diagrams help students map the forces acting on an object in physics. They are used often when studying and applying Newton’s laws of motion. A clear diagram makes it easier to analyze a system before solving for motion. Start by drawing the object under consideration. If the object is treated like a particle, show it as a point and place that point at the origin of an x-y coordinate system. Then add every force that acts on the object as a vector. Do not include the net force on the...

free body diagrams: examples

Free Body Diagram Force Examples

Free body diagrams show the external forces acting on an object or system. The object is drawn as a single isolated point, or free body, so the forces are easier to analyze. Only forces that come from outside the object or system are included. These forces are shown as vectors pointing away from the free body. A person sitting on a chair is a simple example. The free-body diagram has two forces. The chair exerts an upward normal force, and gravity pulls downward with the weight. A rocket sled...

inertial frames of reference

Newton's First Law and Reference Frames

Newton's first law helps identify inertial reference frames. An inertial reference frame is one in which Newton's first law holds true. In that frame, an object with no net force moves at constant velocity. A key idea is that any frame moving at constant velocity relative to an inertial frame is also inertial. For that reason, inertial frames can be found by comparing motion from one frame to another. The laws of physics do not give one inertial frame special status over another. In nature, a...

non-inertial frames of reference

A non-inertial frame of reference is a frame that accelerates, decelerates, or rotates relative to an inertial frame. In these frames, motion can look unusual because the observer is moving with the system. That is why an airplane taking off, a car turning a corner, a merry-go-round, and a tropical cyclone can all be examples of non-inertial motion. These situations can show inertial forces, which seem to appear because the frame itself is accelerating or rotating. The force does not come from...

centrifugal force

Rotating Frames and Pseudo Forces

Pseudo forces, also called fictitious forces, appear in a rotating frame of reference when compared with an inertial frame. They are not real forces. Instead, they are mathematical tools that help make Newton&amp;#39;s laws of motion easier to use in a non-inertial frame. Common examples include centrifugal, Coriolis, and Euler forces. These forces matter in mechanics, astrophysics, and fluid dynamics. In these areas, motion is often described from a frame that is not inertial. That is why...

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key terms and concepts

Explore how accelerating, decelerating, and rotating frames change the way motion looks, from cars and merry-go-rounds to Coriolis force and hurricanes.

Why Motion Seems Different in Accelerating Frames | JoVE K12

physics

JoVE Core 物理学は、運動学、力学、流体力学、静力学、波動、音響などの基礎的な物理学の理論と応用を、簡潔でわかりやすいアニメーション ビデオで紹介します。さらに、科学者の実際のビデオでは、世界中の今日の研究所で行われている古典的および独自の研究実験における関連概念の適用を示しています。

Louisiana Student Standards for Science

High School

motion-and-stability-forces-and-interactions

Motion And Stability: Forces And Interactions

HS-PS2-2

HS-PS2-3

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

Forces And Motion

Motion

Tennessee Academic Standards

Motion and Stability: Forces and Interactions

PHYS.PS2.14

Virginia  Standards of Learning

HIgh School

PS.8

PS.8.b

PH.3

PH.3.a

Next Generation Science Standards

Florida Department of Education

SC.912.P.12

SC.912.P.12.3

SC.912.P.12.8

SC.912.P.12.9

Texas Essential Knowledge and Skills

PHYS.5

PHYS.5.C

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Forces and Interactions

HS-PS2-1.

Newton's Second Law

Newton&#39;s second law is closely related to his first law of motion. It mathematically gives the cause-and-effect relationship between force and changes ...

Second Law: Motion under Same Force

Newton&#39;s laws can be applied to bodies at rest and bodies in motion. Newton&#39;s first law is applied to bodies in equilibrium, whereas the second ...

second-law-motion-under-same-acceleration

Second Law: Motion under Same Acceleration

Newton&#39;s second law of motion applies to bodies moving under the same acceleration. For example, when a baggage tractor pulls luggage carts, each cart ...

Students who demonstrate understanding can analyze data to support the claim that Newton's second law of motion describes the mathematical relationship among the net force on a macroscopic object, its mass, and its acceleration.  Clarifying Statement: Examples of data could include tables or graphs of position or velocity as a function of time for objects subject to a net unbalanced force, such as a falling object, an object sliding down a ramp, or a moving object being pulled by a constant force.  Assessment Boundry: Assessment is limited to one-dimensional motion and to macroscopic objects moving at non-relativistic speeds.

3.2.9-12.I

Inertial Frames of Reference

Newton&#8217;s first law is usually considered to be a statement about reference frames. It provides a method for identifying a special type of reference ...

A reference frame accelerating or decelerating relative to an inertial frame is a non-inertial frame. To help understand this, consider what taking off in ...

Linear Momentum

The term momentum is used in various ways in everyday language, most of which are consistent with the precise scientific definition. Generally, momentum ...

Conservation of Momentum: Introduction

The total momentum of a system consisting of N interacting objects is constant in time or is conserved. A system must meet two requirements for its ...

Conservation of Momentum: Problem Solving

Solving problems using the conservation of momentum requires four basic steps:

	Identify a closed system, where the total mass is constant, and no net ...

Students who demonstrate understanding can use mathematical representations to support the claim that the total momentum of a system of objects is conserved when there is no net force on the system.  Clarifying Statement: Emphasis is on the quantitative conservation of momentum in interactions and the qualitative meaning of this principle.  Assessment Boundry: Assessment is limited to systems of two macroscopic bodies moving in one dimension.

Students who demonstrate understanding can apply scientific and engineering ideas to design, evaluate and refine a device that minimizes the force on a macroscopic object during a collision. Clarifying Statement: Examples of evaluation and refinement could include determining the success of the device at protecting an object from damage and modifying the design to improve it. Examples of a device could include a football helmet or a parachute. Assessment Boundry: Assessment is limited to qualitative evaluations and/or algebraic manipulations.

3.2.9-12.K

Gravitation

In the years before Newton, a general belief prevailed that different laws governed objects in the sky than objects on Earth. When Kepler wrote down the ...

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Newton's Law of Gravitation

Our everyday observation tells us that all objects close to the Earth naturally tend to fall to the ground. Early philosophers assumed that this downward ...

Electric Charges

From lightning during thunderstorms to electronic devices, the phenomenon of electromagnetism is all around us. The electromagnetic force is one of the ...

sources-and-properties-of-electric-charge

Sources and Properties of Electric Charge

All objects we see around us consist of atoms, which combine to form molecules. The lightest element in the universe is hydrogen, and a hydrogen atom ...

Coulomb's Law

Experiments with electric charges have shown that if two objects each have an electric charge, they exert an electric force on each other. The magnitude ...

the-principle-of-superposition-and-the-gravitational-field

The Principle of Superposition and the Gravitational Field

The principle of superposition applies to gravitational forces of objects that are sufficiently far apart. It states that the net gravitational force on a ...

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Electric Field

Consider two point charges, each exerting Coulomb force on the other. It is possible to describe the Coulomb interaction via an intermediate step by ...

Magnetic Fields

A moving charge or a current creates a magnetic field in the surrounding space, in addition to its electric field. The magnetic field exerts a force on ...

Magnetic Field due to Moving Charges

A stationary charge creates and interacts with the electric field, while a moving charge creates a magnetic field.
Consider a point charge moving with a ...

Electromagnetic Fields

Electric fields generated by static charges, often referred to as electrostatic fields, are characteristically different from electric fields created by ...

Students who demonstrate understanding can use mathematical representations of Newton's Law of Gravitation and Coulomb's Law to describe and predict the gravitational and electrostatic forces between objects. Clarifying Statement: Emphasis is on both quantitative and conceptual descriptions of gravitational and electric fields. Assessment Boundry: Assessment is limited to systems with two objects.

3.2.9-12.L

Energy Transfer in Chemical Reactions

Chemical reactions require sufficient energy to cause the matter to collide with enough precision and force that old chemical bonds can be broken and new ...

Batteries and Fuel Cells

A battery is a galvanic cell that is used as a source of electrical power for specific applications. Modern batteries exist in a multitude of forms to ...

Students who demonstrate understanding can plan and conduct an investigation to provide evidence that an electric current can produce a magnetic field and that a changing magnetic field can produce an electric current. Clarifying Statement: N/A Assessment Boundry: Assessment is limited to designing and conducting investigations with provided materials and tools.

3.2.9-12.M

Why Motion Seems Different in Accelerating Frames

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