## circular motion and centripetal force

Brentzoom
Posts: 3
Joined: Mon Oct 08, 2018 9:58 am

### circular motion and centripetal force

centripetal acceleration correspond to acceleration which points in, i.e. a=v^2/r

In training, military piots are given various tests. one test puts them in a seat on the end of a long arm of length 5m which is then spun around ar a high speed.
at top speed the pilot will experience a centripetal force equivalent to six times hiss own weight
calculate he speed of the pilot in this test
calculate the number of revolutions of the pilot per minute

I did this:

set forces equal

6mg = mv^2/r

6g=v^2/r
6gr=v^2

6*9.8*5=v^2
v= 17

for part b I used v=rw

17=5w
w=3.4

I'm not sure if what I did is correct I'm not sure how I can prove the number of revolutions is right

jeff
Posts: 38
Joined: Mon Mar 05, 2018 11:54 pm

### Re: circular motion and centripetal force

HI Brentzoom,
Brentzoom wrote:
Mon Oct 08, 2018 4:04 pm
centripetal acceleration correspond to acceleration which points in, i.e. a=v^2/r

In training, military piots are given various tests. one test puts them in a seat on the end of a long arm of length 5m which is then spun around ar a high speed.
at top speed the pilot will experience a centripetal force equivalent to six times hiss own weight
calculate he speed of the pilot in this test
calculate the number of revolutions of the pilot per minute

I did this:

set forces equal

6mg = mv^2/r

6g=v^2/r
6gr=v^2

6*9.8*5=v^2
v= 17
Yes, this part is correct. I got 17.15 m/s for the speed.

Brentzoom wrote:
Mon Oct 08, 2018 4:04 pm
for part b I used v=rw

17=5w
w=3.4

I'm not sure if what I did is correct I'm not sure how I can prove the number of revolutions is right
This is correct so far, but is not finished yet. What you found so far is the angular speed, which is in radians per second, and the problems asks for revolutions per minute. So you have to convert the radians to revolutions, and the seconds to minutes.

Do you see how to do that? if so, what do you get for the final answer?

Brentzoom
Posts: 3
Joined: Mon Oct 08, 2018 9:58 am

### Re: circular motion and centripetal force

I divided by 6.28 to get the revs
thn divided by 60 to get minutes

is the right? i got 0.009 in revs/minute

jeff
Posts: 38
Joined: Mon Mar 05, 2018 11:54 pm

### Re: circular motion and centripetal force

Brentzoom wrote:
Mon Oct 08, 2018 5:04 pm
I divided by 6.28 to get the revs
thn divided by 60 to get minutes

is the right? i got 0.009 in revs/minute
Almost! dividing by 6.28 is correct (because we have to divide by 2 pi), but to convert seconds to minutes we have to multiply by 60, not divide. That's because the time unit of seconds is below in the denominator, so we need to have seconds in the numerator to cancel that (which will give minutes in the denominator). So it goes like this:

$\frac{3.4\&space;\mbox{rad}}{\mbox{s}}\times\frac{1\&space;\mbox{rev}}{2\pi\&space;\mbox{rad}}\times\frac{60\&space;\mbox{s}}{1\&space;\mbox{minute}}$

In the above equation, the units of s will cancel in the top and bottom, and the units of rad will cancel top and bottom, so what we are left with is rad/min.

Brentzoom
Posts: 3
Joined: Mon Oct 08, 2018 9:58 am

thx