How fast does the Earth need to move to provide centripital acceleration

In summary, the conversation focuses on solving various problems related to the Earth's rotation, including determining the centripetal acceleration at the equator and at different latitudes, finding the required speed for the Earth to rotate for the centripetal acceleration to be equal to gravity, and calculating the required speed for an object to perform uniform circular motion around the Earth. The main confusion arises in trying to determine the necessary centripetal acceleration as a function of latitude. The solution is found to be trivial and not dependent on the angle, meaning that the angle is irrelevant in this scenario.
  • #36
Makonia said:
No I got 6000 and something s, your formula looks wrong so you should try to do it again
I think i figured it out, i used wrong radius, i forgot to add up the radius of the Earth as well :s, i now got 6170 s, is that the same as u got?
 
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  • #37
hefalomp said:
I think i figured it out, i used wrong radius, i forgot to add up the radius of the Earth as well :s, i now got 6170 s, is that the same as u got?
No, I got a little bit more. You used this equation: T = 2*pi*r / (sqrt(G*M/r)?
 
  • #38
Yes, might be that that is wrong then? But you said that (G*M*m)/r^2 is the force and since F=m*a where a=v^2/r you can solve the problem by solving it for v and then setting in the formula for T instead. Can i not use that (G*M*m)/r^2 = m* v^2/r, and solv it for v, then put v in T = 2*pi*r/v ?
 
  • #39
hefalomp said:
Yes, might be that that is wrong then? But you said that (G*M*m)/r^2 is the force and since F=m*a where a=v^2/r you can solve the problem by solving it for v and then setting in the formula for T instead. Can i not use that (G*M*m)/r^2 = m* v^2/r, and solv it for v, then put v in T = 2*pi*r/v ?
I guess we have just done it differently. I got the formula: T=sqrt((4*pi^2*r^3)/(G*M))
 
  • #40
You have used the same formula. One formula is just simplified
 
  • #41
Makonia said:
I guess we have just done it differently. I got the formula: T=sqrt((4*pi^2*r^3)/(G*M))
Even when I use your formula i also get 6170 seconds, do you use r = 7271000 , M = 5,97219*10^24 and G = 6.67408*10^-11 ?
 
  • #42
r is 7,3*10^6
 
  • #43
hefalomp said:
Even when I use your formula i also get 6170 seconds, do you use r = 7271000 , M = 5,97219*10^24 and G = 6.67408*10^-11 ?
No I use the values for r, M and g stated in the task. In other words M=6*10^24, r = 7300*10^3 and I used G with two decimals
 
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  • #44
Makonia said:
No I use the values for r, M and g stated in the task. In other words M=6*10^24, r = 7300*10^3 and I used G with two decimals
Well, that's explanes why i got wrong, i searched for the radius and mass of Earth on google, didnt se that they were mentioned in the task :) Now i should get the right answear..
 
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