Radial and transeverse acceleration

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SUMMARY

The discussion centers on the relationship between radial and transverse acceleration versus tangential and normal acceleration in the context of a particle traveling along a smooth curve. Participants confirm that both sets of terms are valid and highlight that normal corresponds to radial and tangential corresponds to transverse. It is established that normal and tangential directions are defined within the Frenet-Serret frame, while radial and transverse are defined in the polar coordinate frame, coinciding only when the curve is circular. The conversation also touches on terminology variations, such as the use of "circumferential" and "azimuthal" for transverse acceleration.

PREREQUISITES
  • Understanding of acceleration components in physics
  • Familiarity with the Frenet-Serret frame
  • Knowledge of polar coordinate systems
  • Basic concepts of circular motion
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  • Study the Frenet-Serret formulas for curvature and torsion
  • Explore the differences between radial and tangential acceleration in circular motion
  • Learn about polar coordinates and their applications in physics
  • Investigate the terminology variations in physics, such as "circumferential" and "azimuthal" acceleration
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Physics students, educators, and professionals in mechanics who seek to deepen their understanding of acceleration components in curved motion.

gianeshwar
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Particle is traveling along a plane smooth curve.At any point an acceleration is
1 . Resultant of radial and transeverse components?
2. Resultant of tangential and normal components?
Are both 1 and 2 valid?
 
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hi gianeshwar! :wink:

tell us what you think, and why, and then we'll comment! :smile:
 
gianeshwar said:
Particle is traveling along a plane smooth curve.At any point an acceleration is
1 . Resultant of radial and transeverse components?
2. Resultant of tangential and normal components?
Are both 1 and 2 valid?
Not only are they valid, but they are both the same thing: normal = radial, and tangential = transverse.
 
no, i think "radial" in this case is from the origin :wink:
 
Chestermiller said:
Not only are they valid, but they are both the same thing: normal = radial, and tangential = transverse.

Normal and tangential are directions in the Frenet-Serret frame. Radial and transverse are directions in the polar coordinate frame. They coincide identically only when the curve is a circle about the polar system's origin.
 
voko said:
Normal and tangential are directions in the Frenet-Serret frame. Radial and transverse are directions in the polar coordinate frame. They coincide identically only when the curve is a circle about the polar system's origin.
I guess I learned something new. I've never heard of transverse used for polar coordinates. I would have called it circumferential. Go figure.

Chet
 
I think it is also called azimuthal. There is also confusion about centripetal, whether it is "radial" or "normal". I have been confused myself :)
 

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