Question

can someone please solve this 4 me

Answer 1

Torque = Moment of Inertia × Angular acceleration.

R = 6400 km (radius of earth)

I = (9.3 × 10^37) units (Moment of Inertia)

1 year = 365 days = 31536000 seconds

w = (7.3 × 10^(-5)) units. (Angular velocity)

Final angular velocity is zero since earth has to be stopped.

So now we find angular acceleration (alpha) needed.

$\alpha = (7.3 \times {10}^{ - 5}) \div 31536000 \\ \alpha = 2.31481481 \times {10}^{ - 12}$
Torque = R×F

I am writing alpha as "a" for the sake of simplicity.

R×F = I×a
F = (I×a)/R

$= (9.3 \times {10}^{37} \times 2.31481481 \times {10}^{ - 12} ) \div (6400 \times {10}^{3}) \\ = 3.36371527 \times {10}^{19}$
So the tangential force required is

3.36371527 × 10^(19) N