# Simple circular motion conceptual question

#### RJLiberator

Gold Member
1. The problem statement, all variables and given/known data

If the speed was doubled, what would the radius and period be to keep the same acceleration?

2. Relevant equations

a = v^2/R
T = 2piR/t

3. The attempt at a solution

So with my understanding it is as follows:
(2v)^2/R
This makes it 4v^2/x = a
since a=v^2/R

Setting this into a proportion
we get
4v^2*R=v^2*x
so 4R=x

Radius must be 4 times larger to support a doubling in speed.

T = 8piR/t

Correct?

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#### paisiello2

Looks like it's correct to me.

• RJLiberator

#### RJLiberator

Gold Member
Yahoooo!!! I did extremely well on this physics exam, many thanks to people like you on this forum.

Cheers.

#### haruspex

Science Advisor
Homework Helper
Gold Member
2018 Award
If the speed was doubled, what would the radius and period be to keep the same acceleration?
It depends what speed is referred to here. Is it the linear speed at the periphery or the angular speed? Maybe you could post the whole question, word for word.

• RJLiberator

#### RJLiberator

Gold Member
Unfortunately, I don't have the question as it was an exam question.

However, the "car" was going at constant speed on the outside (atan=0?) and the speed was doubled according to arad from my memory.

#### BvU

Science Advisor
Homework Helper
You also have a T = 2piR/t
and you think it changes to T = 8piR/t

But forgot to mention what it T is or what t is. Dimensionally, this looks suspicious.

• RJLiberator

#### RJLiberator

Gold Member
Hm.
T = period.
period = 2pir/time right?

When the r becomes 4R it becomes 8pi*R/t
the only part i am unsure about there is the denominator, t for time, if it is needed.

#### NascentOxygen

Mentor
Hm.
T = period.
period = 2pir/time right?

When the r becomes 4R it becomes 8pi*R/t
the only part i am unsure about there is the denominator, t for time, if it is needed.
The calculation of period will involve speed.

#### RJLiberator

Gold Member
Yes, wouldn't the units be 2piR = meters and t = seconds
so m/s ?

#### NascentOxygen

Mentor
Period is measured in seconds.

#### RJLiberator

Gold Member
Ah.... I see my error, I was under the impression that the definition of period was T = 2piR/t however, that is incorrect. The definition is actually
V = 2piR/T which becomes 2piR/V = T and in my case it would be 8piR/2v which simplifies to 4piR/v and the units becomes m/m/s which is just seconds.

Ah, that is unfortunate, I won't score 100% because i had the wrong definition in my head :p.

Thank you.

#### BvU

Science Advisor
Homework Helper
So if the acceleration stays the same, and the speed while making a turn doubles, the radius has to become four times as big. And the time needed to complete the turn doubles.

• RJLiberator

#### RJLiberator

Gold Member
Indeed. Thank you for that understanding. :)

#### Jediknight

trying to help here but it seems most questions I know are quickly answered, from where I'm standing the only algebra was sqauring your two and moving your centripittal acceleration equation around, then you just plugged those values in for T, if you happen to confuse T equation and did everything else right I doubt your teacher will dock you too much

• RJLiberator

#### RJLiberator

Gold Member
Thanks Jediknight. Yeah, I'm not too bothered, I'm very happy with how the exam went :D

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