How Long Must Zorch Push to Extend Earth's Rotation to 29 Hours?

[blimkie]

i need help with this problem


N.B. See eq. 13.26 and table 13.2 on p.382

11. [1pt] Zorch, an archenemy of Superman, decides to slow Earth's rotation to once per 29.0 h by exerting an opposing force at the equator and parallel to it. Although Superman knows that Zorch can only exert a force of 4.65×107 N (a little greater than a Saturn V rocket's thrust), he isn't sure if it is an immediate concern. Assuming that Earth's moment of inertia for such a process is 9.71×1037 kg·m2 and that its radius is 6.37×106 m, how long would Zorch have to push with this force to accomplish his nefarious goal?

Heres what i did so far..

here is the equation shown in the book a = T/I

a=angular acceleration
T=net torque
I=moment of inertia

so i determned the acceleration is 4.789x10^-31 m/s^2

then i used v=(2)(pi)(r)/T to find the veocity of Earth with the periods of rotation at 24 hours and 29 hours

v at 24h = 1.667x10^6 v at 29h = 1.379x10^6

so then i used the formula

Vf = Vf + a(t) i solved for t and my answer was 6.01 x10^35

when i entered my answer into the online homework grading system it was wrong and i have checked my work and ended up with the same answer twice so i guess I am just using the wrong approach

if anyone could help me that's great thanks

 

[durt]

When you calculated the angular acceleration, you forgot to consider the radius of the earth. And this is angular acceleration, so its units are radians/second^2. After you've found this, you can calculate the time it takes for the Earth to reach its new angular velocity by using the angular equivalent of the equation you selected: $$\omega=\omega_0 + \alpha t$$.

P.S. One way to make this problem (and others in the future) easier is to use symbols until you reach the final equation, into which you can plug in all the given information. That way, you won't be fumbling with big crazy numbers all over the place, and it will be easier to see mistakes.