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

When a particle moves along a curved trajectory, its motion can be described using tangential and normal components. Both the components are attached to the particle and move with it.
For the n-axis, the curved path of the particle is split into multiple different arc segments. Each segment forms the arc of a circle having a radius of curvature and a center of curvature.
The n-axis is normal to the t-axis, and its positive sense points towards the center of the curvature, defined with unit vector un.
The positive of the t-axis is defined along the increasing position of the particle on the path, and it is denoted using a unit vector, ut.
The particle&#39;s velocity is always tangent to the path of the curvilinear motion and has only a t-component.
Differentiating velocity expression with time gives the acceleration of the particle. Here, ut changes at each instant, and its change denotes the direction of un.
This means that for curvilinear motion, the acceleration of the particle has both tangential and normal components

curvilinear motion: normal and tangential components

Curvilinear Motion: Normal and Tangential Components

When a car traverses a curved road, its motion can be elucidated by breaking it down into tangential and normal components. The car-centric coordinates attached to the vehicle move with it.
The positive direction of the t-axis aligns with the increasing position of the car along the curved path, denoted by the unit vector ut. Simultaneously, the n-axis, perpendicular to the t-axis, dissects the curved path into differential arc segments, each forming the arc of a circle with a radius of curvature and a center of curvature. The positive direction of the n-axis points toward the center of curvature, designated by the unit vector un.
On the other hand, the normal component is related to the curvature of the road. The n-axis, perpendicular to the t-axis, is involved in dissecting the curved path into tiny differential arc segments. Each of these segments forms the arc of a circle with a specific radius of curvature and a center of curvature. The positive direction of the n-axis points towards the center of this curvature and is defined by the unit vector un. This component helps describe how the car is deviating from a straight-line path due to the curvature of the road.
The car&#39;s velocity remains tangent to the road, possessing only a t-component. By differentiating the velocity expression with respect to time, the car&#39;s acceleration is derived. Importantly, ut undergoes changes at each instant, indicating the changes in the direction of un.
In essence, for curvilinear motion, the car&#39;s acceleration manifests in both tangential and normal components, providing a comprehensive understanding of how the vehicle navigates along the curved trajectory.

When a particle moves along a curved trajectory, its motion can be described using tangential and normal components. Both the components are attached to ...

curvilinear-motion-normal-and-tangential-components

Education

JoVE Core

Mechanical Engineering

Unit 1

Kinematics of a Particle

KEY TERMS AND CONCEPTS

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...

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

Description

Transcript

Tags