Radial acceleration around a planet

[anteaters]

Homework Statement

Consider a planet of radius 7.31 x 10^6 m with a rotation period of 25.4 hours. Compute the radial acceleration of a point on the surface of the planet at the equator owing to its rotation about its axis.

Homework Equations

T = [2(pi)r]/v
a_r = -[(v^2)/r]

The Attempt at a Solution

so i know one period (T) is 25.4 hours, and r = 7.31 x 10^6 m. so i use that and find velocity, and tried to plug that into the radial acceleration equation, but i got the wrong answer. what am i doing wrong? is it something to do with units of time?

 

[anteaters]

oh, and my answer was 2.88 x 10^8 m/s2

 

[D H]

what am i doing wrong? is it something to do with units of time?

Did you convert the hours to seconds? If not, you are spot-on regarding time.

oh, and my answer was 2.88 x 10^8 m/s2

That means you did something else wrong in addition to the time units error. Please show your work.

 

[anteaters]

25.4 hours = 91440 seconds = 2(pi)(7.31 x 10^6)/v
so v = 502.3 m/s
a_r = [(502.3 m/s)^2]/(7.31 x 10^6) = 0.0345 m/s^2

would that be the right answer? it seems kind of small.

 

[D H]

Looks fine to me.

 

[anteaters]

thanks a lot D H.