Question

I know I can calculate average power by using the work done perunittime.

I thought I could also use (for a rotational problem) torquetimesangular velocity.

I tried to use torque times angular velocity for thefollowingproblem and got it wrong. Why?

Calculate the average power required to accelerate the Earth in4days from rest to its present qngular speed about its axis.

I used I = 2/5 MR² = 9.71e37 kg m ², ω=7.27e-5 rad/s , α = 2.104e-10 rad/s²,
τ = 2.04e28 N m ; KE = 2.57e29 J

If I use P = KE/t I get P = 7.42e23 W, if I use P = τ (dot)ω I getP = 1.48e24 W

Why aren't they equal? What am I missing?