Finding acceleration from position vector with cos and sin terms

[thereddevils]

Homework Statement

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.

Homework Equations

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 ?

 

[cartonn30gel]

Can you please try to correct the latex code?

 

[thereddevils]

Can you please try to correct the latex code?

ok better now ?

 

[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:

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

 

[thereddevils]

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:

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

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

 

[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?

 

[thereddevils]

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?

thanks , nope that's the full question