Understanding Rotational Motion: Answers for Jade

[Jadenag]

Okay so my mechanics teacher is taking a rather mathematical approach to CM and its really confusing me. Can someone explain to me what this actually means?

d hat{r}/dt=dot{theta} hat{theta} and

d hat{theta}/dt=-dot{theta} hat{r}

I mean I know that anything with a hat on top is a unit vector and i also know that theta dot represents angular speed. Thankyou.

-jade

 

[I like Serena]

Hi Jadenag!

Okay so my mechanics teacher is taking a rather mathematical approach to CM and its really confusing me. Can someone explain to me what this actually means?

${d \hat{r} \over dt}=\dot{\theta} \hat{\theta}$ and

${d \hat{\theta} \over dt}=-\dot{\theta} \hat{r}$

I mean I know that anything with a hat on top is a unit vector and i also know that theta dot represents angular speed. Thankyou.

-jade

Yes, $\hat r$ is the local unit vector in the r direction at some point (r, theta).
We could also write $\hat r(r, \theta)$, since it is a function of r and theta.
However, if theta increases a little bit (by $d\theta$), that unit vector changes.
To be precise its angle changes by $d\theta$.

Perhaps you can make a drawing of it and consider which vector represent the change in $\hat r$?