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Torque needed to accelerate Earth

  1. Oct 31, 2004 #1
    Calculate the torque required to accelerate the Earth in 3 days from rest to its present angular speed about its axis

    I got that the Earth's mass is 5.98 X 10^24 kg and its radius is 6.38 X 10^6 m.

    I used that the earth is solid sphere with a moment of inertia of:

    I = 2/5*M*r^2 so then the Earth's moment of inertia would be: 9.74 X 10^37 kg*m^2.

    To get torque i used T=(alpha)I, alpha being dw/dt, so I used (alpha)=(2pi)/(259200 s). 259200 seconds in three days.

    I get the wrong torque, so what is wrong?
     
  2. jcsd
  3. Oct 31, 2004 #2

    arildno

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    I can't see where you're wrong.
    It might be that your book has made the dreadful mistake of using degrees rather than radians, though.
    That's about what I can offer you..
     
  4. Oct 31, 2004 #3
    It's online hw so I know right away my answer is wrong, I get a torque of 2.36e33 Nm. I'm lost as to where I went wrong.
     
  5. Oct 31, 2004 #4

    arildno

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    Hmm.. I think I've found your mistake:
    [tex]\omega_{e}=\frac{2\pi}{24h}=\frac{2\pi}{86400s}[/tex]
    [tex]3days=3*(86400s)[/tex]
    Hence,
    [tex]\alpha=\frac{2\pi}{259200*86400s^{2}}[/tex]
    Hence, your answer should be reduced by a factor 86400.
     
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