Name: curvilinear motion: position, velocity, acceleration
Uploaded: 2024-03-07T13:22:14.000Z
Duration: 1 min 23 s
Channel: JoVE

Curvilinear motion is a type of motion where a particle or an object moves along a curved path involving changes in direction.
If the object is at point A, its position vector is defined using a fixed frame of reference. Here, the ratio of the position vector with its magnitude represents the unit vector in the direction of the position vector.
As the object moves forward, its position changes with time. The velocity of the object is calculated by taking the time derivative of the position vector. Here, for the fixed frame of reference, the direction of unit vectors does not change with time.
Here, the velocity vector can be expressed using rectangular components, and dividing it with the magnitude of velocity vectors gives the unit vector along the direction of the velocity vector.
Taking the time derivative of the velocity vector gives the acceleration vector for the object in rectangular components.
Dividing the acceleration vector with its magnitude gives the unit vector along the direction of the acceleration vector.

curvilinear motion: rectangular components

Curvilinear Motion: Rectangular Components

Curvilinear motion characterizes the movement of a particle or object along a curved path, notably evident when envisioning a car navigating a winding road. If the car starts at point A, its position vector is established within a fixed frame of reference, where the ratio of the position vector to its magnitude signifies the unit vector pointing in the position vector&#39;s direction.
As the car advances, its position evolves over time. Quantifying the car&#39;s velocity involves computing the time derivative of the position vector. Notably, in the fixed frame of reference, the direction of unit vectors remains constant over time.
The velocity vector, expressing the car&#39;s speed and direction, can be dissected into rectangular components. Dividing this vector by its magnitude unveils the unit vector along the direction of the velocity of the car, akin to the car&#39;s heading on the curved road.
Further, taking the time derivative of the velocity vector gives the acceleration vector, representing how the car&#39;s speed or direction changes with time. Normalizing this acceleration vector by its magnitude yields the unit vector for the acceleration of the car, disclosing the direction of the car&#39;s acceleration. In essence, these principles provide a conceptual framework for understanding the intricacies of a car engaged in curvilinear motion.

Curvilinear motion is a type of motion where a particle or an object moves along a curved path involving changes in direction.
If the object is at point ...

curvilinear-motion-rectangular-components

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JoVE Core

Mechanical Engineering

Unit 1

Kinematics of a Particle

KEY TERMS AND CONCEPTS

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 change with time. The velocity vector can also be split into rectangular components, which shows its speed and direction in a clear way.

The unit vector for velocity is found by dividing the velocity vector by its magnitude. This unit vector points in the same direction as the object’s motion, just like the car’s heading on the curved road. The acceleration vector comes from the time derivative of the velocity vector. It shows how the car’s speed or direction changes over time.

The acceleration vector can also be normalized by its magnitude to give the unit vector for acceleration. That unit vector shows the direction of the car’s acceleration. Together, the position, velocity, and acceleration vectors give a simple framework for understanding curvilinear motion.

Curvilinear Motion: Position, Velocity, Acceleration

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

curvilinear-motion-normal-and-tangential-components

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...

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 curvilinear motion through position, velocity, and acceleration vectors, including unit vectors and rectangular components for a car on a curved path.

Curvilinear Motion: Position, Velocity, Acceleration | 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.

Curvilinear Motion: Position, Velocity, Acceleration

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