Name: rotating frames and pseudo forces
Uploaded: 2023-05-16T08:18:40.000Z
Duration: 1 min 6 s
Channel: JoVE

K12 Standards

Tennessee Academic Standards

High School

Physics

motion-and-stability-forces-and-interactions

Motion and Stability: Forces and Interactions

PHYS.PS2.14

Centrifugal Force

なぜボールが回転するメリーゴーランドで外側に飛ぶのか疑問に思ったことはありませんか?
メリーゴーランドが回転すると、ボールは円を描く道をたどります。ひもの張力の成分は、ボールの円運動に必要な求心力を提供します。
求心力は円の中心に向けられ、オブジェクトの質量、角速度の2乗、および回転軸からの距離の積で表されます。
ボールは外側に飛ぶため、ニュートンの第3法則から、内側への求心力は等しく反対の外向きの反力を持つべきであるということになります。回転の中心から離れる方向に向けられたこの外側の力は、遠心力と呼ばれます。
メリーゴーランドで回転するボールは、回転の中心から外側に押し出される遠心力を受けます。
遠心力は疑似力です。これは、観測フレームが非慣性である場合にのみ考慮されます。

<ol>
	<li>ジャンコリ、DC(2014)。物理原理とアプリケーション。カリフォルニア州サンフランシスコ:ピアソン。付録C。</li>
	<li>OpenStaxです。(2019). 大学物理学 Vol.1.【Web版】pp.298.<a href="https://openstax.org/books/university-physics-volume-1/pages/6-3-centripetal-force"から取得>https://openstax.org/books/university-physics-volume-1/pages/6-3-centripetal-force</a></li>
</ol>

利益相反は宣言されていません。

遠心力

擬似的な力、つまり架空の力は、慣性基準系に対して回転する基準系内で動いている物体に作用するように見えます。 これらの力は実際の力ではなく数学的構造であり、ニュートンの運動法則を使用しながら非慣性系での計算を簡素化するために導入されています。 擬似力の一般的な例には、遠心力、コリオリ力、オイラー力などがあります。 これらの力は、非慣性基準系での物体の運動が頻繁に発生する力学、天体物理学、流体力学などの分野では不可欠です。

水平面内で回転する紐に結び付けられたボールを考えてみましょう。 ニュートンの運動の第 1 法則によれば、慣性座標系から観察すると、ボールは直線的に移動します。 ただし、ストリングの張力により継続的に向心力が発生し、ボールが円形の軌道を移動し続けます。 すべての動きは実際の力とニュートンの運動法則のみを使用して適切に記述できるため、この慣性系では遠心力は必要ありません。

次に、ボールと同じ軸の周りをボールと一緒に回転する基準系を考えてみましょう。 このフレームから見ると、ボールは静止しています。 ただし、ストリングの張力または向心力は、回転軸に向かってボールに作用します。

これは、ニュートンの運動法則に矛盾します。これによれば、ボールは正味で加えられる力の方向、つまり回転軸に向かって加速しなければなりません。 向心力と同じ、または反対の遠心力を導入すると、問題は解決されます。 ボールにかかる正味の力はゼロであるため、ボールは回転座標系内で静止したままになります。

ニュートンの最初の 2 つの法則を使用して正しい運動方程式を定式化するには、架空の力が必要です。 ただし、架空の力は、等しい力と反対の力が同じ基準枠内に存在することを要求するニュートンの第 3 法則に従いません。 これは、遠心力と向心力は作用力と反力ではないことを意味します。

疑似力、または架空の力は、慣性基準系に対して回転する基準系で動いている物体に作用するように見えます。...

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Education

JoVE Core

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

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 pseudo forces are useful when analyzing rotating systems and other moving reference frames.

A simple example is a ball tied to a string and whirled in a horizontal circle. From an inertial frame, the ball would move in a straight line if the string were not pulling on it. The tension in the string provides the centripetal force, which keeps the ball moving in a circular path. In this frame, centrifugal force is not needed because the motion can be explained using real forces and Newton&amp;#39;s laws.

Now look at the same ball from a frame rotating with it around the same axis. In that rotating frame, the ball appears stationary. The tension still acts toward the axis of rotation, which would seem to conflict with Newton&amp;#39;s laws. Adding a centrifugal force equal in size and opposite in direction to the centripetal force makes the net force zero and keeps the ball at rest in the rotating frame.

Fictitious forces are therefore needed to write correct equations of motion with Newton&amp;#39;s first two laws in non-inertial frames. They do not obey Newton&amp;#39;s third law. That means centrifugal and centripetal forces are not an action-reaction pair, because the equal and opposite forces must be in the same frame of reference.

Rotating Frames and Pseudo Forces

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

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...

centrifugal force

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...

key terms and concepts

Explore pseudo forces in rotating frames, including centrifugal force, centripetal force, and why a spinning ball stays at rest in the rotating frame.

Rotating Frames and Pseudo Forces | 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。

Virginia  Standards of Learning

HIgh School

Physical Science

PS.8

PS.8.b

PH.3

PH.3.a

Arizona Science Standards

HS+Phy.P3

HS+Phy.P3U1.3

new-york-state-science-learning-standards

New York State Science Learning Standards

HS. Forces and Interactions

HS-PS2-1.

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 ...

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 ...

Electric Field Lines

The three-dimensional representation of the electric field of a positive point charge requires tracing the electric field vectors, whose lengths decrease ...

Properties of Electric Field Lines

The definition of electric field lines greatly eases the visualization of electric fields, a vector field, especially in the presence of many charges. The ...

comparison-between-electrical-and-gravitational-forces

Comparison Between Electrical And Gravitational Forces

There are four fundamental forces in nature: the gravitational force, the electromagnetic force, the strong nuclear force, and the weak nuclear force. To ...

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 ...

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 ...

coulomb-s-law-and-the-principle-of-superposition

Coulomb's Law and The Principle of Superposition

Coulomb&#39;s Law describes the force experienced by two point charges under each other&#39;s presence. But what if there are more than two charges? For ...

Describe and mathematically determine the electrostatic interaction between electrically charged particles using Coulomb’s law. Compare and contrast Coulomb’s law and gravitational force, notably with respect to distance. Describe and mathematically determine the electrostatic interaction between electrically charged particles using Coulomb’s law. Compare and contrast Coulomb’s law and gravitational force, notably with respect to distance. EXPLANATION: Comparisons should note that both of these forces decrease proportional to the square of the distance and both are field interactions. Due to the nature of electric charge, it is possible that coulombic forces can be either attractive or repulsive depending on the charges, while gravitational forces are attractive. Descriptions of electrostatic fields should also include field line diagrams representing both strength and direction of the field in space.

PHYS.PS2.10

Conservation of Energy

The terms &#39;conserved quantity&#39;&#160;and &#39;conservation law&#39;&#160;have specific scientific meanings in physics, which differ from the ...

Conservation of Energy: Application

When solving problems using the energy conservation law, the object (system) to be studied should first be identified. Often, in applications of energy ...

Conservation of Mechanical Energy

The mechanical energy E of a system is the sum of its potential energy U and the kinetic energy K of the objects within it. What happens to this ...

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Work-energy Theorem

According to Newton&#x2019;s second law of motion, the sum of all the forces acting on a particle (net force) determines the rate of change in the ...

Work and Energy for Variable Forces

When an object is acted upon by a variable force, the amount of work done and the change in energy of the object can be more complex to calculate compared ...

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work-energy-theorem-for-motion-along-a-curve

Work-Energy Theorem for Motion Along a Curve

The work-energy theorem can be generalized to the motion of a particle along any curved path. The simple argument here is that the curved path can be ...

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Frictional Force

When a body is in motion, it encounters resistance because the body interacts with its surroundings. This resistance is known as friction, a common yet ...

Static and Kinetic Frictional Force

One of the simpler characteristics of sliding friction is that it is parallel to the contact surfaces between systems, and is always in a direction that ...

Develop and apply the impulsemomentum theorem along with scientific and engineering ideas to evaluate and refine a device that minimizes the force on an object during a collision. Develop and apply the impulsemomentum theorem along with scientific and engineering ideas to evaluate and refine a device that minimizes the force on an object during a collision. EXPLANATION: This topic can be related to conservation of energy and workenergy theorem to explore that bringing an object to rest requires a set amount of energy to be dissipated. By increasing the stopping distance of the object during the time when the force is applied, the required force is decreased since the total work done on the stopping object remains constant. Students can design systems to maximize the stopping distance and in turn decrease the force required to stop the object. Working with constraints on their designs provides students an opportunity to make design decisions in applying their scientific knowledge.

PHYS.PS2.11

Mass and Weight

Mass and weight are often used interchangeably in everyday conversation. For example,&#160; medical records often show our weight in kilograms, but never ...

Weightlessness

When an object is dropped, it accelerates toward the center of the Earth. If the net external force on the object is its weight, it is said to be in free ...

Apparent Weight

True weight is the measure of the gravitational force acting on an object. However, if the object accelerates, its measured weight is different from its ...

Drag Force and Terminal Speed

An interesting force in everyday life is the force of drag on an object when it is moving in a fluid. Like friction, the drag force always opposes the ...

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Use experimental evidence to demonstrate that air resistance is a velocity dependent drag force that leads to terminal velocity. Use experimental evidence to demonstrate that air resistance is a velocity dependent drag force that leads to terminal velocity.      EXPLANATION:  In performing such an experiment, students should treat air resistance as the dependent variable and must therefore be able to manipulate this variable. This can be done by considering a force diagram for an object falling at its terminal velocity. (PHYS.PS2.5) Doing so will reveal that the drag force is equal to the weight force. By varying the weight, the drag force is also varied. If an object with a significant air resistance is used, the terminal velocity can be determined when dropping the object from a significant height. (Note: A common misconception is to treat drag force and weight force as a third law pair. This is incorrect.)

PHYS.PS2.12

Drawing Free-body Diagrams: Rules

The first step in describing and analyzing most phenomena in physics involves the careful drawing of a free-body diagram. Free-body diagrams are useful in ...

Free Body Diagrams: Examples

Solving problems that involve forces is easy using free-body diagrams. A free-body diagram is a sketch showing all the external forces that are acting on ...

Projectile Motion

An object thrown in the air follows a parabolic path under the influence of Earth&#39;s gravitational force. The motion of such an object is called ...

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Projectile Motion: Equations

Projectile motion is commonly observed in our day-to-day life. For example, a basketball thrown by a player, an arrow shot from a bow, and kids jumping ...

Projectile Motion: Example

The theory of projectile motion is very useful for players of several sports to improve their performance. For example, a javelin thrower needs to throw ...

Develop a model to predict the range of a two-dimensional projectile based upon its starting height, initial velocity, and angle at which it was launched.Develop a model to predict the range of a two-dimensional projectile based upon its starting height, initial velocity, and angle at which it was launched. EXPLANATION:  Focus should center on the understanding that horizontal and vertical forces act independently of each other.  Students may develop this idea using video capture tools (cell phones, tablets, web cams) which permit frame by frame analysis. Working with an object of known size as reference in frame, students can develop function for motion in the x and y separately. Use of free-body diagrams can be included to permit separate analysis of each component. Related predictions such as maximum height or situations where the launch height is at a different height than the landing/impact location should also be included. A scale model can be created for the motion of a projectile using strings of varying lengths to affix washers along a meter stick at equal intervals. With such a model, tradeoffs between height and distance can be observed as the initial launch angle is varied.

PHYS.PS2.13

principle-linear-impulse-momentum-for-single-particle-problem

Principle of Linear Impulse and Momentum for a Single Particle: Problem Solving

Consider a massless pulley system consisting of a wooden box and a cylinder of known masses. Determine the speed of the attached objects at a specific ...

Non-uniform Circular Motion

In&#160;uniform circular motion, the particle executing circular motion has a constant speed, and the circle is at a fixed radius. However, not all ...

Dynamics of Circular Motion

An object undergoing circular motion, like a race car, is accelerating because it is changing the direction of its velocity. This centrally directed ...

Dynamics Of Circular Motion: Applications

Suppose a car moves on flat ground and turns to the left. The centripetal force causing the car to turn in a circular path is due to friction between the ...

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 ...

Non-inertial Frames 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 ...

Pseudo forces, or fictitious forces, appear to act on an object in motion in a rotating frame of reference with respect to an inertial reference frame. ...

Plan and conduct an investigation to provide evidence that a constant force perpendicular to an object’s motion is required for uniform circular motion (F = mV^2/r).  Plan and conduct an investigation to provide evidence that a constant force perpendicular to an object’s motion is required for uniform circular motion (F = mV^2/r).  EXPLANATION:  Circular motion requires a balance of two factors: a velocity which will carry an object forward and a force perpendicular to the object’s velocity. This perpendicular force will cause the object’s trajectory to curve inwards in the direction of the force, while continuing to travel forward.  Building on a student’s understanding of projectile motion, it should be made evident that the object’s velocity will not change as there is no component to the force parallel to the object’s motion. Investigations can be performed by selecting variables which students hypothesize will have an effect on the motion of an object moving in a circular pattern. If force sensors are available, this lab can be done by measuring the centrally directed force. Without force sensors, students can perform their investigation using a loose string passing through the center of a hollow tube. A measured hanging mass on the loose end of the string can be used to determine the tension force when the uniform circular motion is achieved. Discussions should also include circular paths that may not be complete circles, such as the apex of a hill or a curve in the road.  (It is essential to clearly distinguish between uniform circular motion and rotational motion.)

Rotating Frames and Pseudo Forces

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