# Tangential & normal vs radial & transverse

• Lifprasir
In summary, the difference between "tangential and normal components" and "radial and transverse components" is that "tangential and normal" are relative to the direction of travel, while "radial and transverse" are usually relative to the origin of the coordinate system.
Lifprasir
What is the difference between "tangential and normal components" and "radial and transverse components" ? I mean in both cases, the two components are perpendicular to each other and one of the components causes the particle to rotated around, the other one gives it a speed to rotate with.

Is it just a matter of different coordinate system, where the tangential + normal are written with respect to cartersian while the radial and transverse is written according to r and theta?.. but other than that, the components do serve the same function right?

There is no difference for circular motion but other types of motion are possible.

"Tangential and normal" are relative to the direction of travel. "Transverse and radial" are usually relative to the origin of the coordinate system, or the centre of some circular symmetry.

shanepitts
Lifprasir said:
What is the difference between "tangential and normal components" and "radial and transverse components" ? I mean in both cases, the two components are perpendicular to each other and one of the components causes the particle to rotated around, the other one gives it a speed to rotate with.

Is it just a matter of different coordinate system, where the tangential + normal are written with respect to cartersian while the radial and transverse is written according to r and theta?.. but other than that, the components do serve the same function right?

If you are using polar coordinates (or spherical or cylindrical coordinates) rather than cartesian coordinates to describe a vector quantity, the basis vectors are not fixed.

The basis vectors for polar coordinates are $\hat r$ and a unit vector in the plane of the vector but perpendicular to $\hat r$ (call it $\hat l$). $\hat r$ is the radial basis vector and $\hat l$ is the transverse basis vector. It may be convenient to analyse rotational motion using polar coordinates.

If you are describing rotational motion of a body you may wish to describe a component of motion that is in the direction of the body's motion and a component that is perpendicular to it. Those components may or may not have the same directions as the radial and transverse basis vectors (which depend not on the direction of motion but on the location of the origin). The normal and tangential components (eg. of velocity or acceleration) will have the same directions as radial and transverse basis vectors if the body's motion is circular about the origin.

AM

A quick Google and Wikipedia search reveals people equating tangential to transverse, and radial to normal, without caveats. Words are ambiguous. How are these words defined in your particular textbook? If your lecturer is using one of these words, ask him *exactly* what he means by it. If you are just pulling them out of thin air then I suggest you find something better to do.

Yes, you are correct in your understanding that the difference between tangential and normal components and radial and transverse components lies in the coordinate system used to describe them. In both cases, these components represent the perpendicular forces acting on a particle, with one component causing rotation and the other providing the speed for rotation.

The tangential and normal components are typically described in a Cartesian coordinate system, where the tangential component is parallel to the direction of motion and the normal component is perpendicular to it. This coordinate system is commonly used in linear motion analysis.

On the other hand, the radial and transverse components are described in a polar coordinate system, with the radial component representing the force acting towards or away from the center of rotation and the transverse component representing the force acting perpendicular to the radial direction. This coordinate system is commonly used in circular motion analysis.

While these components may serve a similar function in terms of describing the forces acting on a particle, the choice of coordinate system depends on the type of motion being analyzed and the most convenient way to describe it. Both systems are equally valid and can be used interchangeably depending on the context.

## What is the difference between tangential and normal velocity?

Tangential velocity refers to the speed of an object traveling along a circular path, while normal velocity refers to the speed of an object traveling perpendicular to that path.

## What is the relationship between radial and transverse velocity?

Radial velocity refers to the component of velocity that is directed towards or away from the center of a circle, while transverse velocity refers to the component that is perpendicular to the radial velocity. They are perpendicular to each other and together make up the total velocity of an object traveling along a circular path.

## How do tangential and normal acceleration differ?

Tangential acceleration refers to the rate of change of tangential velocity, while normal acceleration refers to the rate of change of normal velocity. Tangential acceleration can change the speed of an object, while normal acceleration changes the direction of an object's velocity.

## What is the formula for calculating radial velocity?

The formula for calculating radial velocity is vr = rω, where vr is the radial velocity, r is the radius of the circle, and ω is the angular velocity.

## Can an object have both tangential and radial velocity at the same time?

Yes, an object traveling along a circular path will have both tangential and radial velocity. The tangential velocity determines the speed at which the object is moving along the path, while the radial velocity determines the direction in which the object is moving towards or away from the center of the circle.

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