Find the curvature?

  • Thread starter Math10
  • Start date
  • #1
301
0

Homework Statement


Find the curvature of r(t)=2ti+2tj+k.

Homework Equations


None.

The Attempt at a Solution


The answer is 0 in the book.
I know the formula for curvature is k(t)=abs(r'(t)xr"(t))/abs(r'(t))^3. I know that r'(t)=2i+2j and r"(t)=0, so r'(t)xr"(t)=0? How to find r'(t)xr"(t) and r'(t)^3?
 

Answers and Replies

  • #2
34,697
6,399

Homework Statement


Find the curvature of r(t)=2ti+2tj+k.

Homework Equations


None.

The Attempt at a Solution


The answer is 0 in the book.
I know the formula for curvature is k(t)=abs(r'(t)xr"(t))/abs(r'(t))^3. I know that r'(t)=2i+2j and r"(t)=0, so r'(t)xr"(t)=0?
Yes.
Math10 said:
How to find r'(t)xr"(t) and r'(t)^3?
r'(t)r''(t) = 0, which you already found. What is |r'(t)|? Note that this means the magnitude or length of r'(t).
 
  • #3
301
0
So how do I find abs(r'(t))? That's where I got stuck.
 
  • #4
SteamKing
Staff Emeritus
Science Advisor
Homework Helper
12,796
1,668
So how do I find abs(r'(t))? That's where I got stuck.
The notation |r'(t)| does not mean the absolute value of r'(t), it means to find the magnitude of the vector r'(t). Think Pythagoras.
 
  • #5
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
2020 Award
35,596
6,458
The notation |r'(t)| does not mean the absolute value of r'(t), it means to find the magnitude of the vector r'(t). Think Pythagoras.
The problem is that Math10 quoted the formula using abs() instead of modulus.
It should be ##k(t)=\frac{|\dot{\vec r}(t)\times \ddot {\vec r}(t)|}{|\dot{\vec r}(t)|^3}##
 
  • #6
34,697
6,399
So how do I find abs(r'(t))? That's where I got stuck.
Three of us have told you that |r'(t)| does not mean "absolute value". It means "magnitude" or "length" of the vector r'(t).
 

Related Threads on Find the curvature?

  • Last Post
Replies
1
Views
596
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
5
Views
7K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
2
Views
838
Replies
4
Views
4K
Replies
1
Views
2K
Replies
1
Views
998
Replies
2
Views
679
Top