Proving Curvature Formulas: V X A / l V3l and a(t) * N(t) / l V(t) I2

In summary, the person is seeking help with proving two curvature formulas. They have a hint from their professor but are still confused and are looking for a YouTube video to help them get started. They mention using the equation a(t) = at * T + an * N to get the first part, but are stuck on converting it to the form of V X A and getting it over the cube of the speed. They also clarify that these are not actual equations as there are no equal signs.
  • #1
Baumer8993
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Homework Statement


I have to prove two of the curvature formulas. The first one is (V X A) / l V3l

The other one is a(t) * N(t) / l V(t) I2


Homework Equations



I have a hint from my professor, but it is all confusing. I need a youtube video or something to get started on these.

The Attempt at a Solution



I used the a(t) = at *T + an*N to get the first part, but now I am stuck on the making it into the form of V X A. The I have no idea how I would get it over the cube of the speed.
 
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  • #2
These don't seem to be equations. There are no equals signs. Can you edit and tell us what you mean?
 

Related to Proving Curvature Formulas: V X A / l V3l and a(t) * N(t) / l V(t) I2

1. What is the purpose of proving curvature formulas?

The purpose of proving curvature formulas is to mathematically describe the amount of curvature present in a given curve or surface. These formulas allow scientists to quantify and analyze the curvature of different shapes and objects, which can be useful in a variety of fields such as physics, engineering, and mathematics.

2. How is the formula V X A / l V3l used to calculate curvature?

The formula V X A / l V3l is used to calculate the curvature of a curve in three-dimensional space. V represents the velocity vector, A represents the acceleration vector, and l V3l represents the magnitude of the velocity vector. This formula is based on the concept of centripetal acceleration, which is the acceleration of an object moving in a circular path.

3. What does the symbol a(t) * N(t) / l V(t) I2 represent in the curvature formula a(t) * N(t) / l V(t) I2?

The symbol a(t) * N(t) / l V(t) I2 represents the curvature vector of a curve at a specific point. a(t) represents the acceleration vector, N(t) represents the normal vector, and l V(t) I2 represents the magnitude of the velocity vector. This formula is based on the concept of tangential acceleration, which is the acceleration of an object moving along a curved path.

4. How do scientists use curvature formulas in their research?

Scientists use curvature formulas in their research to analyze and understand the shape and properties of different objects and surfaces. These formulas can be applied to various fields, such as studying the curvature of the Earth's surface in geography, or determining the optimal curvature for a bridge in engineering. They can also be used to solve complex mathematical problems involving curves and surfaces.

5. Are there any limitations to using curvature formulas?

While curvature formulas can provide valuable information about the curvature of a given shape or object, they do have some limitations. These formulas assume that the curves and surfaces being analyzed are smooth and continuous, which may not always be the case in real-world scenarios. Additionally, curvature formulas only provide a mathematical description and do not take into account other factors such as material properties or external forces acting on the object.

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