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Rotational motion

  • Thread starter Jadenag
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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
 

Answers and Replies

  • #2
I like Serena
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Hi Jadenag! :smile:

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?

[itex]{d \hat{r} \over dt}=\dot{\theta} \hat{\theta}[/itex] and

[itex]{d \hat{\theta} \over dt}=-\dot{\theta} \hat{r}[/itex]

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

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

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