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

The motion of a particle in a curvilinear path can be described using the normal and tangential components.
The normal component is directed along the normal (or radial) path to the curve at a particular point. It depicts the variation in the trajectory of the velocity vector.
The tangential component is tangential to the curve at a specific point and characterizes the rate at which speed changes along the path.
The equation of motion for a particle in a curvilinear motion can be expressed using Newton&#39;s second law of motion along normal and tangential components.
Here, positive tangential acceleration represents an increase in the magnitude of the speed, and negative tangential acceleration represents a decrease in the magnitude of the speed of the particle.
On the other hand, the normal component of the acceleration is always along the radius of the curved path, and it is positive when directed towards the center of the curvature. The normal component of the force is also defined as centripetal force.

equations of motion: normal and tangetial components

Equations of Motion: Normal and Tangetial Components

Describing the motion of a particle along a curvilinear path involves understanding its components in terms of normal and tangential aspects. The normal component aligns with the radial direction of the curve at a specific point, reflecting changes in the trajectory of the velocity vector. In contrast, the tangential component is tangential to the curve at that point and signifies the rate at which speed alters along the path.
Newton&#39;s second law of motion is employed to articulate the equation of motion for a particle undergoing curvilinear motion, considering both normal and tangential components. Positive tangential acceleration indicates an increase in the magnitude of the speed, while negative tangential acceleration signifies a reduction in the particle&#39;s speed.
In this context, the normal component of acceleration always aligns with the radius of the curved path. When directed towards the center of curvature, it is considered positive. Furthermore, the normal component of force is identified as the centripetal force, establishing a crucial connection between the particle&#39;s dynamics and its curvilinear trajectory. This comprehensive approach facilitates a nuanced examination of particle motion within a curvilinear framework.

The motion of a particle in a curvilinear path can be described using the normal and tangential components.
The normal component is directed along the ...

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

Education

JoVE Core

Mechanical Engineering

Unit 1

Kinetics of a Particle: Force and Acceleration

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

KEY TERMS AND CONCEPTS

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...

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

Description

Transcript

Tags