# Vector problem

1. Jun 3, 2010

### thereddevils

1. The problem statement, all variables and given/known data

A particle moves so that its position vector r at the time t is given by
$$r=s(\cos \omega t \theta+\sin \omega t j)$$ with s and omega as constants. (j is meant to be a vector here)

(1)Show that the acceleration of the particle is $$-\omega r^2$$.

(2) Show that the acceleration of the particle is perpendicular to its velocity.

2. Relevant equations

3. The attempt at a solution

(1) To find the acceleration vector, i guess i will need to differentiate the position vector twice. But i am not sure how to differentiate that.

r=s cos omega t theta + s sin omega t j

i don see any i vectors here ?

Last edited: Jun 3, 2010
2. Jun 3, 2010

### cartonn30gel

Can you please try to correct the latex code?

3. Jun 3, 2010

### thereddevils

ok better now ?

4. Jun 3, 2010

### cartonn30gel

What I understand from this is that the first part is in tangential direction and the second part is along some linear axis, possibly the y-axis. Is that correct?

Here is what I mean:

$$r=s(\cos(\omega t) \hat{\theta}+\sin(\omega t) \hat{j})$$

5. Jun 3, 2010

### thereddevils

thanks , could you explain a little further on the part undergoing tangential direction?

normally, i come across vectors with i and j direction but never with theta direction so i am not so familiar with that

6. Jun 4, 2010

### cartonn30gel

Tangential direction means this: Say you are moving on some arbitrary path (most possibly some curve) The direction of your instantaneous velocity is the tangential direction at that instant of time. So unlike the linear axes (x,y,z) there is no set tangential direction; it changes as you change your path.

However, notice that there is also a variable "t" in this equation. Are you given anything that relates t to theta in any way?

7. Jun 4, 2010

### thereddevils

thanks , nope thats the full question