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

• Michael_0039
In summary, helicoidal movement is a type of motion where an object moves along a curved path while also rotating around an axis, creating a helix or spiral-like pattern. The acceleration vector in this type of movement is a combination of tangential and normal components. Arc length can be calculated using the formula S = rθ, where S is the arc length, r is the radius of curvature, and θ is the angle of rotation. The radius of curvature is the radius of the circle that best fits the curve at a specific point and is used to measure the amount of curvature in a helix. Helicoidal movement can be observed in various natural and man-made processes and is also utilized in engineering and design.
Michael_0039
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... :)

Helicoidal movement

PeroK
I think that's correct.

Michael_0039

## 1. What is helicoidal movement?

Helicoidal movement is a type of motion in which an object moves along a curved path while also rotating around a central axis. This results in a helix or spiral-like trajectory.

## 2. What is the acceleration vector in helicoidal movement?

The acceleration vector in helicoidal movement is the sum of two components: tangential acceleration, which is the rate of change of the object's speed along the curved path, and centripetal acceleration, which is the acceleration towards the central axis due to the object's rotation.

## 3. How is arc length calculated in helicoidal movement?

Arc length in helicoidal movement can be calculated using the formula S = ω * r * t, where S is the arc length, ω is the angular velocity, r is the radius of the helix, and t is the time.

## 4. What is the radius of curvature in helicoidal movement?

The radius of curvature in helicoidal movement is the radius of the circle that best fits the curved path of the object at a given point. It is affected by the object's speed, angular velocity, and the curvature of the path.

## 5. How does helicoidal movement differ from circular motion?

In circular motion, the object moves along a circular path with a constant speed and a fixed radius. In helicoidal movement, the object's speed and radius can vary, and it also has an additional rotational component around a central axis.

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