Name: curved motion: tangential and normal forces
Uploaded: 2024-03-07T13:22:17.000Z
Duration: 1 min 10 s
Channel: JoVE

曲線パス内の粒子の運動は、法線成分と接線成分を使用して記述できます。
法線コンポーネントは、法線(または半径)パスに沿って特定のポイントのカーブに向けられます。これは、速度ベクトルの軌跡の変動を示しています。
接線成分は、特定のポイントで曲線に接し、パスに沿って速度が変化する速度を特徴付けます。
曲線運動における粒子の運動方程式は、法線成分と接線成分に沿ったニュートンの運動の第二法則を使用して表すことができます。
ここで、正の接線加速度は速度の大きさの増加を表し、負の接線加速度は粒子の速度の大きさの減少を表します。
一方、加速度の法線成分は常に曲線パスの半径に沿っており、曲率の中心に向けられると正になります。力の法線成分は、求心力としても定義されます。

運動方程式: 法線成分と接線成分

Equations of Motion: Normal and Tangetial Components

曲線パスに沿った粒子の動きを記述するには、法線方向と接線方向の観点からそのコンポーネントを理解する必要があります。 法線コンポーネントは、特定の点でカーブの半径方向に位置合わせされ、速度ベクトルの軌道の変化を反映します。 対照的に、接線成分はその点での曲線の接線方向であり、経路に沿った速度の変化率を表します。

ニュートンの運動の第 2 法則は、法線成分と接線成分の両方を考慮して、曲線運動する粒子の運動方程式を明確にするために使用されます。 正の接線加速度は速度の大きさの増加を示し、負の接線加速度は粒子の速度の減少を示します。

この文脈では、加速度の法線成分は常に曲線経路の半径と一致します。 曲率の中心に向けられた場合、それは正であるとみなされます。 さらに、力の法線成分は向心力として特定され、粒子のダイナミクスとその曲線軌道の間の重要な関係が確立されます。 この包括的なアプローチにより、曲線の枠組み内での粒子の動きの微妙な検査が容易になります。

曲線パス内の粒子の運動は、法線成分と接線成分を使用して記述できます。
法線コンポーネントは...

equations-of-motion-normal-and-tangetial-components

Education

JoVE Core

Mechanical Engineering

機械工学

Unit 1

ユニット1

Kinetics of a Particle: Force and Acceleration

質点の動力学：力と加速度

kinetics-of-a-particle-force-and-acceleration

KEY TERMS AND CONCEPTS

主要用語と概念

curved motion: tangential and normal forces

Curved motion is described by splitting a particle’s acceleration into tangential and normal parts. These two components help show how the particle moves along a curving path at a specific point.

The tangential component lies along the curve. It shows how the speed changes with time. A positive tangential acceleration means the speed is increasing. A negative tangential acceleration means the speed is decreasing.

The normal component points along the radial direction of the curve. It describes the change in the direction of the velocity vector. This component always follows the radius of the curved path. When it points toward the center of curvature, it is taken as positive.

Newton’s second law is used to write the equation of motion for this kind of motion. The normal force component is called centripetal force. Together, the normal and tangential components give a clear picture of particle motion along a curvilinear path.

Curved Motion: Tangential and Normal Forces

curved-motion-tangential-and-normal-forces

equations of motion: rectangular coordinates and cylindrical coordinates

equations-motion-rectangular-coordinates-cylindrical

Particle Motion in Rectangular and Cylindrical Form

Particle motion can be written in rectangular coordinates or cylindrical coordinates, depending on the path of the particle. In classical mechanics, the coordinate system you choose helps describe how a particle moves in an inertial frame. When motion stays in the x-y plane, rectangular components are often enough. Using only x and y makes the equation easier to write and follow. This form works well for motion that does not need a third spatial direction. Curved paths often call for...

equations of motion: normal and tangetial components

Curved motion is described by splitting a particle’s acceleration into tangential and normal parts. These two components help show how the particle moves along a curving path at a specific point. The tangential component lies along the curve. It shows how the speed changes with time. A positive tangential acceleration means the speed is increasing. A negative tangential acceleration means the speed is decreasing. The normal component points along the radial direction of the curve. It...

normal and tangetial components: problem solving

normal-and-tangetial-components-problem-solving

Chair Reaction Forces in Curvilinear Motion

Chair reaction forces in curvilinear motion are found by using tangential and normal components of acceleration. A 70 kg man sits upright in a chair that is connected to a pin support by member BC. The member is 10 m long, and it makes a 45° angle with the horizontal at the instant of interest. The man has a speed of 5 m/s, and that speed is increasing at 1 m/s². The tangential acceleration is therefore 1 m/s². The normal acceleration is then determined from the tangential speed and the radius...

equation of motion: center of mass

Center of Mass and System Motion

The center of mass helps describe the motion of a system of particles. For a group with n particles, the equation of motion can be extended from a single particle to the whole system. Each particle has a net force on it that comes from both internal forces and external forces. When the motion of all particles is combined, the system follows one equation of motion. Forces between pairs of particles are internal forces. These forces act along the same line, have equal magnitude, and point in...

central-force motion

Central Force Motion and Areal Velocity

Central force motion describes the path of an object acted on by a force that points toward a fixed point, usually the origin. The force size depends on how far the object is from that point. For a mass m, the motion is written in polar coordinates, which use distance and angle instead of x and y position. In this system, the azimuthal component of force is zero. That means there is no force in the angular direction. When the equation of motion is rewritten and integrated, the product of the...

key terms and concepts

Learn how Newton’s second law describes curved motion with tangential and normal components, including speed change and centripetal force.

Curved Motion: Tangential and Normal Forces | 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。

Curved Motion: Tangential and Normal Forces

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