Helicoidal movement: acceleration vector, arc length, radius of curvature

Click For Summary
SUMMARY

The discussion centers on helicoidal movement, specifically addressing the acceleration vector, arc length, and radius of curvature. Participants confirm the correctness of the initial understanding of helicoidal motion. The conversation emphasizes the importance of accurately defining these parameters in the context of physics and mathematics. No alternative suggestions were provided, indicating a consensus on the topic's interpretation.

PREREQUISITES
  • Understanding of basic physics concepts related to motion
  • Familiarity with calculus, particularly derivatives and integrals
  • Knowledge of vector analysis
  • Concept of curvature in geometry
NEXT STEPS
  • Research the mathematical formulation of helicoidal movement
  • Explore the relationship between acceleration vectors and curvature
  • Study applications of helicoidal motion in engineering
  • Learn about the implications of arc length in three-dimensional motion
USEFUL FOR

Students and professionals in physics, mathematics, and engineering who are studying motion dynamics and the properties of helicoidal trajectories.

Michael_0039
Messages
59
Reaction score
7
Homework Statement
The position of a material point in a Cartesian coordinate system 0XYZ given from the equation r=( 3sin(t) , 3cos(t) , 4t ), t : time. Describe in a few words the motion and find the route's length (arc length) from t=5 to t=10. Calculate the accelerattion vector and the radius of curvature at every point on the track.
Relevant Equations
r = ( 3sin(t) , 3cos(t) , 4t )
I have tried to solve it and I would like a confirmation, correction or if something else is suggested... :)

1.jpg


2.jpg
1568626083892.png

Helicoidal movement
 
  • Like
Likes   Reactions: PeroK
Physics news on Phys.org
I think that's correct.
 
  • Like
Likes   Reactions: Michael_0039

Similar threads

Prove that the field due to a circular arc is same as its bounded tangent at the centre of curvature
  • · Replies 23 ·
Replies
23
Views
1K
Electric Field from a Charged Semicircular Rod
  • · Replies 2 ·
Replies
2
Views
3K
The components of force and velocity vectors in circular motion
  • · Replies 11 ·
Replies
11
Views
3K
Dynamics of Circular Motion
  • · Replies 12 ·
Replies
12
Views
995
Determining the final velocity and acceleration magnitude traveling along an arc
  • · Replies 3 ·
Replies
3
Views
6K
MHB Formula to find arc radius using arc length, chord length, and/or segment angle
  • · Replies 4 ·
Replies
4
Views
6K
Undergrad A set of numbers as a smooth curved changing manifold.
  • · Replies 3 ·
Replies
3
Views
3K
Finding the radius of a Proton's arc inside a square.
  • · Replies 2 ·
Replies
2
Views
1K
Why can't we do this by using radius of curvature?
  • · Replies 2 ·
Replies
2
Views
1K
Stretched spring attached to the center of a pure rolling disk
  • · Replies 11 ·
Replies
11
Views
1K