Help Solving Dynamics Angle of Gear!!!

Question

Ok the problem states "The moments of inertia of gears A and B are IA = 0.02 kg-m^2 and IB = 0.09 kg-m^2. Gear A is connected to a torsional spring with constant k = 12 N-m/rad. If gear B is given an initial counterclockwise angular velocity of 10 rad/s with the torsional spring unstretched, through what maximum counterclockwise angle does gear B rotate?"

Gear B has a radius of 140 mm and Gear A has a radius of 200mm. They are grinding against each other, so Gear B is moving counterclockwise and Gear A is moving clockwise. The answer given in the back of the book is .731 rad = 41.9 degrees.

My prof hinted to solve use Conservation of Energy equation

1/2IBwB^2 1/2IAwA^2 0 = 0 (1/2k * theta^2)

and rAwA = rBwB

I used these equations and did not get the right answer...i ended up with 1.04 = theta. Help make this clear to me!! I'm completely lost!

Answer 1

initial gear B angular velocity of 10 rad/s.

Gear B has a radius of 140 mm and Gear A has a radius of 200mm.

gear A angular velocity = 140/200 gear B angular velocity

initial gear A angular velocity = 7/10 x 10 rad/s = 7 rad/s.

initial kinetic energy = 0.5 x 0.02 x 7^2 + 0.5 x 0.09 x 10^2

At maximum angle spring energy = 0.5 x 12 x theta^2

0.5 x 12 x theta^2 = 0.5 x 0.02 x 7^2 + 0.5 x 0.09 x 10^2

12 x theta^2 = 0.02 x 7^2 + 0.09 x 10^2

theta^2 = 0.831667 = 499/600

theta = sqrt(499/600) = 0.9119576

The spring is connected to gear A, so gear A maximum angle = 0.9119576.

gear B angle = 10/7 gear A angle = (10/7)(0.9119576) = 1.30 rad.

I don't get your answer or the book's answer. I have triple checked my calculations and don't find any mistakes. Can you?