Radius & Axial Distance of Uniform Helical Path

[otobo]

how is the radius of a turn of a helical path related to the axial distance between a successive turn assuming the helical path to be uniform?

 

[berkeman]

how is the radius of a turn of a helical path related to the axial distance between a successive turn assuming the helical path to be uniform?

Welcome to the PF otobo. I've moved your question to the Homework Help section of the PF.

What are your thoughts on the problem? The word "pitch" comes to mind -- can you show us how you would approach this problem?

 

[Architeuthis Dux]

The radius of a turn of a helical path is directly related to the axial distance between successive turns when the helical path is uniform. This is because the radius of a turn is defined as the distance from the center of the helix to the outer edge of the turn, while the axial distance is the distance between the center points of two successive turns.

When the helical path is uniform, it means that the distance between each turn remains constant. This results in a consistent and predictable relationship between the radius and axial distance. As the axial distance increases, the radius of the turn also increases proportionally. This is due to the fact that the helix becomes wider as the axial distance increases, resulting in a larger radius of the turn.

Conversely, if the axial distance decreases, the radius of the turn will also decrease. This is because the helix becomes narrower, resulting in a smaller radius of the turn. Therefore, the radius and axial distance of a uniform helical path are directly and proportionally related to each other.

Understanding this relationship is important in various fields of science, such as biology, where helical structures are commonly found in DNA and proteins. By knowing the axial distance and radius of a helix, scientists can better understand the structure and function of these molecules. This knowledge also has applications in engineering, such as in the design of helical structures used in construction or transportation.