Centripetal Acceleration formula derivation

  • #1
36
0

Main Question or Discussion Point

Hello,
This is a very basic question. I am sure I am doing something wrong in the derivation as shown in the picture. But I am not able to find out where I am doing it wrong. It would be very helpful if you can pls. let me know what I am doing wrong here.
Thanks
 

Attachments

Answers and Replies

  • #2
Doc Al
Mentor
44,892
1,144
You calculate the distance traveled in Δt. Why? And then you set that distance equal to the change in velocity? Why again?
 
  • #3
36
0
You calculate the distance traveled in Δt. Why? And then you set that distance equal to the change in velocity? Why again?
Because in Δt, the velocity changes from v0 to v. And for small change in time this can be equal to the distance traveled because of the triangle similarities. That is what the assumption is behind the effort. Can you pls. elaborate where you find something wrong or missing ?
 
  • #4
2
1
Actually,the assumption that for a small time interval, the change in velocity is equal to the distance travelled is wrong.
 
  • #5
Doc Al
Mentor
44,892
1,144
Because in Δt, the velocity changes from v0 to v. And for small change in time this can be equal to the distance traveled because of the triangle similarities. That is what the assumption is behind the effort. Can you pls. elaborate where you find something wrong or missing ?
A change in velocity cannot equal a distance. You can use similar triangles: ##\frac{\Delta v}{v} = \frac{\Delta x}{r}##. Use that and you can easily derive the formula.
 
  • #6
36
0
A change in velocity cannot equal a distance. You can use similar triangles: ##\frac{\Delta v}{v} = \frac{\Delta x}{r}##. Use that and you can easily derive the formula.
I got it now. It has to be the ratio...Thanks a lot
 

Related Threads on Centripetal Acceleration formula derivation

Replies
7
Views
1K
Replies
43
Views
7K
Replies
5
Views
687
Replies
1
Views
714
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
1
Views
15K
Replies
13
Views
14K
Replies
7
Views
110K
Top