Question

I don't see any variable t so how do I find the derivative with respect to t? And do I need to rearrange the equation to have theta as the subject? (picture) @John_ES

Answer 1

Hi.......the equation given to you is of the curve (path followed by the particle) - so obviously you won't have t in it

Answer 2

What you need to do is : Assume del(r) as a straight line (because it is a very small distance on the curve) which is being travelled by the particle at speed v. The change in angle that will take place when the particle travels from r to r + del(r) will be del(theta)

Answer 3

Hmmm. Or am I supposed to use the chain rule to get dtheta/dt?

Answer 4

that IS the way .....Above I gave the explanation for the question ....u know dr/dt =v (constant speed)
and you can find dtheta/dr from the equation
Use chain rule

Answer 5

to find dtheta/dt .......you can surely then find the second derivative.........but don't do this blindly........try to understand first what is dr and dtheta

Answer 6

Alright now I have the first derivative. Do I do the same process for the second?

Answer 7

differentiate your first derivative again - you will get your second derivative :P

Answer 8

But isn't the first derivative still in terms of theta? Since dtheta/dt used was an implicit derivative?

Answer 9

Because I have dr/dt = -k sin theta dtheta/dt

Answer 10

Wait for now I only have dr/dt, not dtheta/dt :/

Answer 11

u can find dtheta/dr from the the equation u have................use chain rule to find dtheta/dt

Answer 12

i gotta go friend..........i m sure u will be able to do the sum on your own now

Answer 13

Alright thanks. I'll try