# Motion in curves - Find radial and circumferential components of V and A

thaer_dude

## Homework Statement

At time t, a comet has the position R = (t2-1)i + 2tj

At t = 2, find the radial and circumferential components of velocity and acceleration

## Homework Equations

Vr = V * Ur
Vθ = V * Uθ

ar = a * Ur
aθ = a * Uθ

Ur = cosθ i + sinθ j
Uθ = -sinθ i + cosθ j

## The Attempt at a Solution

I've found

v = 2ti + 2j
a= 2i

However, am I allowed to use these equations when the position vector is a function of t and not a function of θ? I'm not very good at polar coordinates so I'm really not sure if I can apply the above equations to my problem right away. Thanks

## Answers and Replies

Homework Helper
so you've found the correct equations for v & a in caretseian coords, however now you must find their projection in the radial and theta directions

thaer_dude
Yeah, but say I do Vr = V * Ur

I would get

Vr = (2t i + 2 j) * (cosθ i + sinθ j)
Vr = 2tcosθ i + 2sinθ j

Is that right? It strikes me as odd that the Vr I found has both θ and t in it.

Homework Helper
Yeah, but say I do Vr = V * Ur

I would get

Vr = (2t i + 2 j) * (cosθ i + sinθ j)
Vr = 2tcosθ i + 2sinθ j

Is that right? It strikes me as odd that the Vr I found has both θ and t in it.

if that is a dot product, then it should have a scalar result, not a vector
Vr = (2t i + 2 j) * (cosθ i + sinθ j) = 2tcosθ + 2sinθ

And it should be a simple exercise to write theta in terms of t

Last edited:
Staff Emeritus
Homework Helper
Gold Member
Yeah, but say I do Vr = V * Ur

I would get

Vr = (2t i + 2 j) * (cosθ i + sinθ j)
Vr = 2tcosθ i + 2sinθ j

Is that right? It strikes me as odd that the Vr I found has both θ and t in it.
What sort of multiplication gives: (2t i + 2 j) * (cosθ i + sinθ j) = 2t*cosθ i + 2sinθ j ?