Homework Help Forum: Physics

Posted by Nikita on Monday, October 26, 2009 at 11:58am.

How long would it take for the Earth to complete a full turn if a person at 49.2° northern geographical latitude floats apparently weightlessly across the room? Use REarth = 6,385 km for the radius of Earth

• Physics - Nikita, Monday, October 26, 2009 at 12:01pm

  How long would it take for the Earth to complete a full turn if a person at 49.2° northern geographical latitude floats apparently weightlessly across the room? Use REarth = 6,385 km for the radius of Earth.

  
  

• Physics - MathMate, Monday, October 26, 2009 at 12:37pm

  Not sure if I understood your question. I interpret it as saying "if the Earth is rotating at a yet unknown angular velocity ω such that a person would float weightlessly at latitude 49.2°N, find &omega." It is not as simple as it sounds, because the acceleration due to gravity acts towards the centre of the Earth. On the other hand, the rotation of the Earth is around a N-S axis, causing the centripetal force to be at an angle θ with the vertical, where θ is the latitude. Assuming that the vertical (towards the centre of the earth) components balance, and the person floating is restrained from flying south by a horizontal rope, then we can do the following calculations: Acceleration due to gravity, g = 9.8 m/s² Radius of the Earth, R = 6385 km = 6385000 m Latitude = 49.2° We will find r, the distance of the surface of the earth to the axis of rotation, i.e. measured along the equatorial plane. r = Rcos(θ) Centripetal acceleration, a = rω² (perpendicular to axis of rotation) Vertical component of centripetal acceleration, av = a cos(θ) = rω² cos(&theta) = Rω&up2; cos2(&theta) Equate av and g, solve for &omega. I get 0.0019 radians/sec. which translats to a full rotation in 55 minutes and 14 seconds.

  
  

• Physics-corr - MathMate, Monday, October 26, 2009 at 12:40pm

  Editorial correction: Vertical component of centripetal acceleration, av = a cos(θ) = rω² cos(θ) = R ω² cos²(θ)

  
  

• Physics-supp. reading - MathMate, Monday, October 26, 2009 at 12:51pm

  Here's an article complete with figures for supplementary reading: http://galitzin.mines.edu/INTROGP/notes_template.jsp?url=GRAV%2FNOTES%2Flatitude.html&page=Gravity%3A%20Notes%3A%20Latitude%20Variations

  
  

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