Name: centripetal acceleration in circular motion
Uploaded: 2023-04-30T10:52:21.000Z
Duration: 1 min 14 s
Channel: JoVE

K12 Standards

north-carolina-k-12-science-standard-course-of-study

North Carolina K-12 Science Standard Course of Study

9-12

Earth and Environmental Science

Earth's Place in the Universe

ESS.EES.1.2

Uniform Circular Motion

円形の経路に沿って移動する物体は、円運動を示すと言われ、円運動は均一または不均一のいずれかです。一様な円運動では、物体は一定の速度で移動します。
軌道を周回する衛星の場合、地球の重力は円運動に必要な求心力を提供します。
衛星の線速度は、どの瞬間でも円形の経路に接しているため、その大きさは一定に保たれますが、方向は異なります。
速度の方向が変化するため、衛星はいつでも半径方向の内側に加速します。この加速度は、求心加速度または半径方向加速度と呼ばれます。
力の方程式をmで割ると、求心加速度の大きさは、速度を地球の中心から衛星までの距離で割ったものの2乗になります。
速度は軌道円周2πrを周期Tで割ったものに等しいため、求心加速度と衛星の時間周期との関係が得られます。

等速円運動

等速円運動は、物体が一定の速度で円を描く特定の種類の運動です。 たとえば、一定の速度で回転するプロペラ上の任意の点は、等速円運動を受けています。 時計の秒針、分針、時針も等速円運動をします。 たとえ回転速度が一定であっても、これらのこれらの回転する物体の点が加速度を持つとは直感的に理解しにくいかもしれません。これを理解するには、動きをベクトルの観点から分析する必要があります。

1 次元の運動学では、速度が一定の物体の加速度はゼロです。 ただし、2 次元および 3 次元の運動学では、速度が一定であっても、粒子が円などの曲線軌道を描いて運動する場合、加速度が生じます。 加速度ベクトルの方向は円の中心に向かう方向です。 これは半径方向の加速度であり、向心加速度と呼ばれます。 求心性（centripetal）」という語は、「中心」を意味するラテン語 *centrum* と、「求める」を意味する *petere* に由来し、「中心へ向かう」という意味になります。向心加速度の大きさは、物体の速さと円軌道の曲率半径によって決まり、幅広い値を取ることができます。

このテキストは <a href="https://openstax.org/books/university-physics-volume-1/pages/4-4-uniform-circular-motion"> Openstax, University Physics Volume 1, Section 4.4: Uniform Circular Motion.</a> から編集されたものです。

一様円運動は、物体が一定の速度で円を描くように移動する特定のタイプの運動です。たとえば、プロペラの任意の点...

Education

JoVE Core

Physics

物理学

Unit 1

ユニット1

Motion in Two or Three Dimensions

2次元および3次元における運動

KEY TERMS AND CONCEPTS

主要用語と概念

centripetal acceleration in circular motion

Uniform circular motion describes motion in a circle at constant speed. An object follows a curved path, but its speed does not change. The motion of a point on a propeller spinning at a steady rate and the second, minute, and hour hands of a watch are common examples.

Even with constant speed, these objects are still accelerating. That idea can seem surprising because in one-dimensional motion, constant speed means zero acceleration. In two- and three-dimensional motion, a particle can accelerate if it moves along a curved path such as a circle.

To understand this motion, the direction of the velocity and acceleration vectors matters. The acceleration points toward the center of the circle. This radial acceleration is called centripetal acceleration, and the term means “center seeking.”

Centripetal acceleration can vary over a wide range. Its value depends on the speed of the object and the radius of the circular path. A faster motion or a tighter curve changes the size of the acceleration.

Centripetal Acceleration in Circular Motion

centripetal-acceleration-in-circular-motion

position and displacement vectors

Describing Motion with Position Changes

Describing motion starts with position. Position tells where an object is at a particular time. It must be measured relative to a frame of reference, which is an arbitrary set of axes used to describe position and motion. Earth is often used as a frame of reference. It helps describe an object’s location in relation to stationary objects on Earth. Many important motions also take place in two dimensions, or in a plane. In those cases, position, velocity, and acceleration can each be described...

average and instantaneous velocity vectors

average-and-instantaneous-velocity-vectors

Position Change and Instant Velocity

Position change and instant velocity are key ideas in kinematics. To describe motion, time must be included. Time tells us where an object is and how fast it is moving. The speed of an object comes from how its position changes with time. Each position is tied to a specific time. When the details of motion at each instant are not important, the rate is given as average velocity. Average velocity is a vector. It equals the total displacement between two points divided by the elapsed time. Real...

acceleration vectors

How Velocity Changes Create Acceleration

Acceleration describes how velocity changes over time. In physics, acceleration is a vector, which means it has both size and direction. It points in the same direction as the change in velocity, written as Δv. The larger the acceleration, the larger the change in velocity over a given time. Because velocity is a vector, it can change in more than one way. An object can speed up, slow down, change direction, or do both at once. A runner traveling 10 km/h due east who stops, turns around, and...

direction of acceleration vectors

Negative Acceleration and Motion Reversal

Acceleration describes a change in velocity. That change can be a change in speed, a change in direction, or both. The acceleration vector points in the direction of the velocity change, not always in the direction the object is moving. When an object slows down, its acceleration points opposite to its motion. This is often called deceleration. The term can be confusing in physics because deceleration is not a vector. It does not give a direction relative to a coordinate system, so the correct...

projectile motion

Projectile Paths Under Gravity

Projectile motion describes the path of an object thrown into the air under Earth’s gravity. The object is called a projectile, and its curved path is called the trajectory. This motion appears in many real situations, such as fireworks, a golf ball in flight, meteors entering Earth’s atmosphere, and bullets being fired. When a falling object has no horizontal movement, it is described as one-dimensional projectile motion. When motion includes both horizontal and vertical parts, it is...

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projectile motion: equations

Solving Projectile Motion with Components

Projectile motion can be solved by breaking the motion into horizontal and vertical components. This approach is used for common examples like a basketball throw, an arrow shot from a bow, and kids jumping into a pool. The motion is then analyzed along the x-axis and y-axis. Start by separating displacement into x and y parts. The horizontal and vertical parts of velocity are also separated. If the projectile has speed v and direction θ relative to the horizontal, the vertical component is...

projectile motion: example

Projectile Motion in Sports and Orbit

Projectile motion helps explain both sports throws and motion near Earth. A javelin thrower uses this idea to send the javelin as far as possible. The thrower also takes a short run-up to increase the initial speed of the javelin. For a projectile on level ground, the range is the horizontal distance it travels. The range is largest at a 45° angle, so javelin throwers try to release the javelin as close to that angle as possible. In this case, the range equation assumes the distance is very...

uniform circular motion

Uniform circular motion describes motion in a circle at constant speed. An object follows a curved path, but its speed does not change. The motion of a point on a propeller spinning at a steady rate and the second, minute, and hour hands of a watch are common examples. Even with constant speed, these objects are still accelerating. That idea can seem surprising because in one-dimensional motion, constant speed means zero acceleration. In two- and three-dimensional motion, a particle can...

non-uniform circular motion

Circular Motion with Changing Speed

Circular motion can happen with changing speed. In this case, the object still follows a circular path, but it may speed up or slow down as it moves. When speed changes during circular motion, the motion is called non-uniform circular motion. This adds tangential acceleration, which points along the path of motion and shows a change in speed. Centripetal acceleration is still present in circular motion. It describes the time rate of change of the direction of the velocity vector and points...

relative velocity in one dimension

Relative Motion in a Train and Earth

Relative motion depends on the reference frame used to measure velocity. A reference frame is the point of view from which motion is described. In many examples, Earth is the reference frame. If someone is said to be sitting in a train moving east at 10 m/s, that speed is measured relative to Earth.

relative velocity in two dimensions

Adding Velocities Across Reference Frames

Relative velocity describes motion as measured from a chosen reference frame. It can also describe the motion of one reference frame compared with another. In two dimensions, this idea helps track how position and velocity change from frame to frame. Consider a particle P and two reference frames, S and S′. The position of the origin of S′, measured in S, and the position of P, measured in S′, can be combined with vector addition to find the position of P in S. This relation shows how motion...

key terms and concepts

Learn how constant-speed motion in a circle still involves acceleration, why the acceleration points inward, and how speed and radius affect centripetal acceleration.

Centripetal Acceleration in Circular Motion | 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。

Texas Essential Knowledge and Skills

High School

PHYS.5

PHYS.5.D

Florida Department of Education

Physical Science

SC.912.P.12

SC.912.P.12.2

Georgia Standards of Excellence

SP2.

Circular Motion

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Centripetal Acceleration in Circular Motion

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