Need help with question regarding circular motion.

Fungamania

Thanks for checking out my thread. Okay, first off, the question.

The earth rotates once per day about an axis passing through the north and south poles, an axis that is perpendicular to the plane of the equator. Assuming the earth is a sphere with a radius of 6.38 X 10^6 m, determine the speed and centripetal acceleration of a person situated (a) at the equator and (b) at a latitude of 30.0° north of the equator.

I'll show what i've done so far.

a) V=2(pi)r/t
plugged in the appropriate values where r is (6.38 x 10^6) and t is (86400).

my results from that equation was 463.97 m/s.

I then continued to calculate the centripetal acceleration:

a=v^2/t
a=(463.97^2)/6.38 x 10^6)
a=0.03 m/s^2
(I wasn't expecting it to be this small.

b) the troubling thing now is obviously the angle. Do I use the following formula?

v=sq(rgtan(theta))
v=sq((6.38 x 10^6)(9.8)(tan30))
v=6,008 m/s

then to caluculate the centripetal accceleration:
a=v^2/r
and I end up getting 5.6 m/s^2


I'm not sure if the answers are correct (most likely not) Any help would be greatly appreciated. Thanks for your time!!

Fungamania

bump, anyone?

thebigeis

Sorry, I don't have anything to help you out with; but I just wanted to tell you your problem helped me solve my problem. Apparently I had incorrect values for the radius of the Earth and the period of the Earth. Thanks, Fungamania.

Integral

You need to reconsider the radius at 30deg. It should be LESS then the radius at the equator. I recommend drawing a picture, or look at a globe to figure out just what the radius is. (in this case it is the distance from the axis of rotation that you need).

Dmstifik8ion

You can give someone a sin but you cannot make them read.

Didia

Find the radius of the smaller circle. for a degree od 30, i got the radius as 5525242.076 m. I am pretty sure it is right, i don't know how to explain it in words. You have to draw it out and find the radius using the coine of 30 times the radius of the earth. Hope it helps. If you still have a question, email me.