Physics HELP!!?

Question

You visit a planet that turns on its axis once every 24 hours. The radius of the planet at its equator is 5.72×106 meters.
You would feel weightless at the equator on this planet, if it rotated fast enough so that the centripetal acceleration at the planet's surface was equal to the acceleration due to gravity (which in this case is 12.5 m/s2). Calculate the new rotational period for this planet necessary to produce this effect! Calculate the period in hours.



(I tried using the equation a=((2*pi*r*f)^2)/r but I get the wrong answer every time.)

Answer 1

This is actually a Newton's second law question with a little gravity thrown in. The forces acting on a person at the equator are the normal force acting outward (away from the planet), gravity, and these two combine to create a centripetal acceleration inward. Writing Newton's Law for this situation we get:

N-mg= - m(w^2)r where N is normal force, w is angular velocity (i cant type the omega symbol here) and r the radius of the planet. The centripetal acceleration is on the right hand side.

Being weightless means you experience no normal force, so if N=0, we have that mg=m(w^2)r; the m's cancel, so we can solve for angular velocity:

w=sqrt[g/r]=sqrt[12.5/5.72x10^6]=0.0015rad/sec
this implies it would take 4248 secs to complete one rotation (2 pi) radians, or 1.18 hours.

Answer 2

sounds like Earth

Answer 3

hmmm i studeied this a coulple of years ago, but i cant really much of it. im in quatum physics now, so if u have a question from that i can awswer that for you!