Name: curved path motion in tangential and normal axes
Uploaded: 2024-03-07T13:22:15.000Z
Duration: 1 min 27 s
Channel: JoVE

当质点沿曲线轨迹运动时，其运动可用切向和法向分量来描述。这两个分量均附着在质点上，并随质点一起运动。
对于 n 轴，粒子的曲线路径被划分为多个不同的弧段。每一段构成一个圆的弧，该圆具有曲率半径和曲率中心。
n轴垂直于t轴，其正方向指向曲率中心，用单位矢量un表示。
正t轴沿路径上粒子位置增加的方向定义，并用单位矢量ut表示。
粒子的速度始终与曲线运动轨迹相切，且仅有切向分量。
对速度表达式关于时间求导可得到粒子的加速度。此处，ut 在每一时刻都发生变化，其变化方向表示 un 的方向。
这意味着在曲线运动中，质点的加速度既有切向分量，也有法向分量

曲线运动:法向分量和切向分量

Curvilinear Motion: Normal and Tangential Components

当汽车行驶在弯曲的道路上时，可以通过将其分解为切向分量和法向分量来阐述其运动过程。其中以汽车为中心的坐标将会随汽车发生移动。

t 轴的正方向与汽车沿弯曲路径所发生变化的位置是一致的，该过程可以用单位向量 u_t 来进行表示。同时，垂直于 t 轴的 n 轴能够将弯曲的路径分割成不同的弧，每个弧段能够形成具有曲率半径和曲率中心的圆弧。 n 轴的正方向指向曲率中心，并且由单位向量 u_n 来进行表示。

另一方面，法向分量与道路的曲率有关。 n 轴垂直于 t 轴，用于将弯曲的路径分割成微小的微分弧段。这些弧段中的每一个都能够形成具有特定曲率半径和曲率中心的圆弧。其中 n 轴的正方向指向该曲率的中心，并且由单位矢量 u_n 来进行定义。该组件有助于描述汽车是如何由于道路曲率而发生偏离直线的路径。

汽车的速度方向是与道路相切的，并且仅具有 t 分量。通过对速度的表达式和时间进行微分，可以得出汽车的加速度。重要的是，u_t 在每时每刻都会发生变化，该公式表明了u_n 方向所发生的变化。

本质上，对于曲线运动，汽车的加速度体现在切向分量和法向分量中，从而能够以此来全面了解车辆是如何沿着曲线运动的轨迹来进行行驶的。

当粒子沿曲线轨迹运动时，其运动可用切向和法向分量来描述。这两个分量均附着于……

curvilinear-motion-normal-and-tangential-components

Education

教育

JoVE Core

Mechanical Engineering

机械工程

Unit 1

第一单元

Kinematics of a Particle

质点运动学

KEY TERMS AND CONCEPTS

关键术语与概念

curved path motion in tangential and normal axes

Curved path motion is described with tangential and normal axes. These car-centered coordinates move with the vehicle as it travels. The t-axis points in the direction of increasing position along the curved path. The n-axis is perpendicular to the t-axis and points toward the center of curvature.

The path can be split into tiny arc segments. Each segment matches part of a circle with a radius of curvature and a center of curvature. The positive n-direction uses the unit vector u n . This normal component shows how the car departs from a straight-line path because of the road’s curvature.

The car’s velocity stays tangent to the road. That means it has only a t-component. When velocity is differentiated with respect to time, the car’s acceleration is found. Because the unit vector u t changes with time, the direction of u n also changes.

As a result, curvilinear motion has both tangential and normal components of acceleration. Together, these components give a fuller picture of how a car moves along a curved trajectory.

Curved Path Motion in Tangential and Normal Axes

curved-path-motion-in-tangential-and-normal-axes

curvilinear motion: rectangular components

curvilinear-motion-rectangular-components

Curvilinear Motion: Position, Velocity, Acceleration

Curvilinear motion describes an object moving along a curved path. A car on a winding road is a clear example. The object’s position is shown with a position vector in a fixed frame of reference. The unit vector for that position comes from the position vector divided by its magnitude. As the object moves, its position changes with time. The velocity vector is found by taking the time derivative of the position vector. In a fixed frame of reference, the directions of the unit vectors do not...

motion of a projectile

Projectile Motion in a Soccer Kick

Projectile motion in a soccer kick shows how a ball travels through the air after it is launched. The launch angle, which is the angle of the kick, plays a major role in shaping the path of the ball. Once the ball is in the air, gravity is the only force acting on it. The ball’s motion can be split into two independent velocity components: horizontal and vertical. The horizontal motion comes from the initial kick and stays at a constant velocity during the flight. Kinematics equations in the...

curvilinear motion: normal and tangential components

Curved path motion is described with tangential and normal axes. These car-centered coordinates move with the vehicle as it travels. The t-axis points in the direction of increasing position along the curved path. The n-axis is perpendicular to the t-axis and points toward the center of curvature. The path can be split into tiny arc segments. Each segment matches part of a circle with a radius of curvature and a center of curvature. The positive n-direction uses the unit vector u n . This...

curvilinear motion: polar coordinates

Radial and Tangential Motion in Polar Form

Polar coordinates describe curvilinear motion using a radial distance and an angle. The radial coordinate, r, extends from a fixed origin to the particle. The angular coordinate, θ, is measured in radians. It gives the counterclockwise angle between a fixed reference line and the radial line to the particle. The particle’s position is written with a unit vector in the radial direction. Taking the time derivative of that position gives the velocity. That velocity has two parts. One is radial,...

key terms and concepts

Explore how a car moving along a curved road is described using tangential and normal axes, with velocity tangent to the path and acceleration split into two components.

Curved Path Motion in Tangential and Normal Axes | 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 Path Motion in Tangential and Normal Axes

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