Circular Motion: Tangential and Normal Acceleration

AI Thread Summary
The discussion focuses on the relationship between tangential acceleration (a_s) and normal acceleration (a_n) in circular motion. Participants explore relevant equations, including a_n = v^2/R and v = v_0 + a_s*t, while seeking a general expression for a_s in relation to v_s. Clarifications indicate that the problem does not require a defined value for v_0 but rather an expression involving variables. The conversation emphasizes the importance of understanding the equations and their applications in circular motion. Overall, the thread highlights collaborative problem-solving in physics.
Heexit
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Homework Statement
A particle moves in a circular path of radius R in such a way that the tangential acceleration is equal to the normal acceleration. Determine the velocity as a function of time t and the initial velocity (v_0).
Relevant Equations
N/A
Hello Physicsforum!

This is my attempt:
First I realised:
##a_s=a_n##

Secondly I used since previus known formulas:
##a_n=\frac {v^2} {R}##
##v=v_0+a_s*t##

Although now I do not know how to continue, any suggestions would be appriciated!
Thanks for your help on beforehand :smile:
 
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Heexit said:
##v=v_0+a_s*t##
That is only if the tangential acceleration has constant magnitude.
What equation relates ##a_s## to ##v_s## more generally?

Unless you have left out some information, there is no way to determine ##v_0##.
 
haruspex said:
That is only if the tangential acceleration has constant magnitude.
What equation relates ##a_s## to ##v_s## more generally?

Unless you have left out some information, there is no way to determine ##v_0##.
Thanks for your help!

The only equation that I can think of is:
##a_s=\frac {dv} {dt}##
Anything more than that I can't think of :/

There might have been some inaccurate translation on my side, sorry about that. The question does not ask us for a define value of ##v_0##, rather an expression of variables, see solution in picture below:
1685002553625.png
 
Heexit said:
The only equation that I can think of is:
##a_s=\frac {dv} {dt}##
That will do nicely. Combine that with your other information.
Heexit said:
The question does not ask us for a define value of ##v_0##, rather an expression of variables, see solution in picture below:
View attachment 327036
Ok.
 
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Likes MatinSAR and Heexit
Thanks for your help!
Here is my solution:
1685006197544.png
 
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