Torque needed to accelerate Earth

[GingerBread27]

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?

 

[arildno]

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..

 

[GingerBread27]

It's online homework 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.

 

[arildno]

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