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

곡선 경로에서 입자의 움직임은 법선 및 접선 구성 요소를 사용하여 설명할 수 있습니다.
법선 구성요소는 법선(또는 방사형) 경로를 따라 특정 점에서 곡선으로 향합니다. 속도 벡터의 궤적 변화를 나타냅니다.
접선 구성요소는 특정 점에서 곡선에 접하며 경로를 따라 속도가 변경되는 속도를 특성화합니다.
곡선 운동에서 입자에 대한 운동 방정식은 법선 및 접선 구성 요소를 따른 뉴턴의 두 번째 운동 법칙을 사용하여 표현할 수 있습니다.
여기서 양의 접선 가속도는 속도의 크기 증가를 나타내고 음의 접선 가속도는 입자 속도의 크기 감소를 나타냅니다.
반면에 가속도의 수직 구성 요소는 항상 곡선 경로의 반지름을 따라 있으며 곡률의 중심을 향할 때 양수입니다. 힘의 수직 구성 요소도 구심력으로 정의됩니다.

 운동 방정식: 법선 및 접선 구성요소

Equations of Motion: Normal and Tangetial Components

곡선 경로를 따라 입자의 움직임을 설명하려면 해당 구성 요소를 법선 및 접선 측면에서 이해해야 합니다. 법선 구성요소는 속도 벡터의 궤적 변화를 반영하여 특정 지점에서 곡선의 반경 방향과 정렬됩니다. 이와 대조적으로 접선 구성요소는 해당 지점에서 곡선에 접하며 경로를 따라 속도가 변경되는 비율을 나타냅니다.

뉴턴의 운동 제2법칙은 법선 성분과 접선 성분을 모두 고려하여 곡선 운동을 하는 입자의 운동 방정식을 명확하게 표현하는 데 사용됩니다. 양의 접선 가속도는 속도 크기의 증가를 나타내고, 음의 접선 가속도는 입자 속도의 감소를 나타냅니다.

이러한 맥락에서 가속도의 일반 구성요소는 항상 곡선 경로의 반경과 일치합니다. 곡률 중심을 향하면 양수로 간주됩니다. 더욱이, 힘의 일반적인 구성 요소는 구심력으로 식별되어 입자의 역학과 곡선 궤적 사이에 중요한 연결을 설정합니다. 이 포괄적인 접근 방식은 곡선 프레임워크 내에서 입자 운동의 미묘한 검사를 용이하게 합니다.

곡선 경로에서 입자의 움직임은 법선 및 접선 구성 요소를 사용하여 설명할 수 있습니다.
일반 구성 요소는 ...

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

Education

교육

JoVE Core

Mechanical Engineering

기계공학

Unit 1

제1단원

Kinetics of a Particle: Force and Acceleration

입자의 운동역학: 힘과 가속도

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

KEY TERMS AND CONCEPTS

주요 용어 및 개념

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 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.

Curved Motion: Tangential and Normal Forces

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