Proving centripetal acceleration formula

  • Thread starter dragon513
  • Start date
  • #1
26
0
Hi I was taught about centripetal accerleration last class, but my teacher didn't tell me why or how this formula works.

So I was wondering if anyone knows a website that has mathematical proof of this formula.

Thanks in advance.
 

Answers and Replies

  • #2
Andrew Mason
Science Advisor
Homework Helper
7,686
403
dragon513 said:
Hi I was taught about centripetal accerleration last class, but my teacher didn't tell me why or how this formula works.

So I was wondering if anyone knows a website that has mathematical proof of this formula.

Thanks in advance.
Have a look at this link:

AM
 
  • #3
Tide
Science Advisor
Homework Helper
3,089
0
What formula are you talking about?

If you mean [itex]a = v^2 / r[/itex] then you may be able to convince yourself with the following:

If an object is undergoing uniform circular motion then

[tex]x = r \cos \omega t[/tex]

[tex]y = r \sin \omega t[/tex]

Now just take derivatives and find the speed [itex]v = \sqrt {\dot x^2 + \dot y^2} = \omega r[/itex]. Likewise, the acceleration is [itex]a = \omega^2 r^2[/itex].

Combine the two to obtain

[tex]a = \frac {v^2}{r}[/tex]

You can generalize this to "nonuniform" circular motion.
 
Last edited:

Related Threads on Proving centripetal acceleration formula

  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
4
Views
1K
Replies
0
Views
2K
Replies
28
Views
571
E
  • Last Post
Replies
1
Views
702
  • Last Post
Replies
5
Views
3K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
15
Views
1K
  • Last Post
Replies
1
Views
767
Top