Im a bit confused about a question on circular motion that i'm answering. Ill state the entire question and then say what im confused about.(adsbygoogle = window.adsbygoogle || []).push({});

In class we discussed circular motion for the case

[tex]\displaystyle{\frac{d\theta}{dt} = \omega}[/tex]

Now assume that the circle has radius [tex]r[/tex] and that

[tex]\displaystyle{\frac{d\theta}{dt} = 2t}[/tex]

for [tex]t[/tex] in seconds. Let [tex]\theta(t = 0) = 0[/tex]

(therefore [tex]\theta = t^2[/tex])

a) Find [tex]\vec{r}(t)[/tex]

b) Find [tex]\vec{v}(t)[/tex]. is [tex]\vec{v} \perp \vec{r}[/tex]?

c) Find [tex]\vec{a}(t)[/tex]. Express [tex]\vec{a}[/tex] in terms of [tex]\vec{r}[/tex] and [tex]\vec{v}[/tex]. Is [tex]\vec{a} \perp \vec{v}[/tex]?

d) With respect to the circle's centre, sketch [tex]\vec{r},\vec{v}[/tex] and [tex]\vec{a}[/tex] for counter clockwise rotation.

Ok. I have found all the vectors in i-j form. My question is about the perpendicularity questions. Mathematically I have found that [tex]\vec{r} \perp \vec{v}[/tex] and that [tex]\vec{a} \perp \vec{v}[/tex]. I have also found that [tex]\vec{a}[/tex] can be written as [tex]-\alpha \vec{r}[/tex] (where [tex]\alpha[/tex] is a constant. All this implies that the acceleration vector is pointed back into the centre of the circle as some negative multiple of [tex]\vec{r}[/tex].

If this is so then how is the particle speeding up?? (the rate of change of theta is time dependent)

I would have thought that the acceleration vector would have been at some angle to the position vector. But then it wouldnt move in a circle.... Im confused....

Also, the second part of (c) im finding hard. Anyone any ideas?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Confusing circular motion

**Physics Forums | Science Articles, Homework Help, Discussion**