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Circular motion question

i cant seem to get the right answer for this question "_" i'm probably making a very basic mistake but i just cant see it lol

A particle travels at a constant speed around a circle of radius r with a centripetal acceleration a. what is the time taken for ten complete rotations?
if:
v=2πrTv=\frac{2 \pi r }{T}

T=2πrvT=\frac{2 \pi r }{v}

and if
a=v2ra= \frac{ v^{2} }{r}

v=arv=\sqrt{ar}
so substitute for V

T=2πrarT= \frac{2 \pi r }{\sqrt{ar}}

T=2πaT= \frac{2 \pi }{\sqrt{a}}
for 10 revolutions so times both sides by 10
10T=20πa10T=\frac{20 \pi }{\sqrt{a}}
Reply 1
anybody?
Original post by cuckoo99
i cant seem to get the right answer for this question "_" i'm probably making a very basic mistake but i just cant see it lol

A particle travels at a constant speed around a circle of radius r with a centripetal acceleration a. what is the time taken for ten complete rotations?
if:
v=2πrTv=\frac{2 \pi r }{T}

T=2πrvT=\frac{2 \pi r }{v}

and if
a=v2ra= \frac{ v^{2} }{r}

v=arv=\sqrt{ar}
so substitute for V

T=2πrarT= \frac{2 \pi r }{\sqrt{ar}}

T=2πaT= \frac{2 \pi }{\sqrt{a}}


The line above is not correct. r does not cancel.
Reply 3
I found this hard tooo
Reply 4
rr\sqrt{r}\neq r therefore the r doesn't cancel.
Reply 5
lolz what a stupid mistake ye i found the answer to be 20πra20 \pi \sqrt{\frac{r}{a} }

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