# Math Help - Uniform Circular Motion Problem

1. ## Uniform Circular Motion Problem

Here is(are) the question(s):

"Find the centripetal acceleration for each of the following:
(a) a point on the earth's equator (ignore its orbital motion);
(b) the earth in its orbit around the sun;
(c) the sun's orbit around the center of the Milky Way (period = 2 x 10^8 y; radius = 3 x 10^20 m"

(a) 3.37 x 10^(-2) m/s
(b) 5.9 x 10^(-3) m/s^
(c) 3 x 10^(-10) m/s

I get (a) ac = 2.97 x 10^(-10) m/s^2 which is wrong. What am I doing wrong?

(My work is attached)

Any help would be greatly appreciated!

2. Originally Posted by s3a
Here is(are) the question(s):

"Find the centripetal acceleration for each of the following:
(a) a point on the earth's equator (ignore its orbital motion);
(b) the earth in its orbit around the sun;
(c) the sun's orbit around the center of the Milky Way (period = 2 x 10^8 y; radius = 3 x 10^20 m"

(a) 3.37 x 10^(-2) m/s
(b) 5.9 x 10^(-3) m/s^
(c) 3 x 10^(-10) m/s

I get (a) ac = 2.97 x 10^(-10) m/s^2 which is wrong. What am I doing wrong?

(My work is attached)

Any help would be greatly appreciated!
First you do not have enough explanation of what you are attempting to do (as a consequence you will not gain any marks for method even though the final answer is wrong).

The centripetal acceteration in uniform circular motion is:

$a=r \dot{\theta}^2$

Here $r\approx 6.38\times 10^6\ \text{m}$ is the Earths radius, and $\dot{\theta}=(2\pi)/(24 \times 60 \times 60) \approx 7.272 \times 10^{-5} \text{radians/second}$ the Earths rotation rate.

so:

$a \approx (6.38\times 10^6)\times (7.272 \times 10^{-5})^2 \approx 0.0337$ $\text{m/s}^2$

CB

3. Thanks for telling me how to get (a) right but why is my method wrong?(Bad logic or bad formula or what? - like why does my method not also work?) (I was trying to find speed using v = (2*pi*r)/T and then pluging v in ac = v^2 /r )

4. Originally Posted by s3a
Thanks for telling me how to get (a) right but why is my method wrong?(Bad logic or bad formula or what? - like why does my method not also work?) (I was trying to find speed using v = (2*pi*r)/T and then pluging v in ac = v^2 /r )
I am tempted to say: How would I know, in the brief look I had it looked confused and I could not be bothered to try and work out what you were trying to do?

It should work so I presume your arithmetic is in error.

CB