How Long Does It Take a Rolling Spool to Hit the Floor?

[willworkforfood]

"A string is wound around a solid cylindrical spool of mass 9.4 kg and radius .11 m. Assume the acceleration of gravity to be 9.8 m/s^2. If the spool is released from rest and rolls along the string and the distance to the floor is 9.06 meters, then how long in seconds will it take the spool to hit the floor?"

I'm having trouble solving this. I tried setting torque equal to torque r*m*g=moment of inertia*(a/r). After I solved for acceleraton I threw it into the linear kinematics equation 9.06=.5*a*t^2 to solve for time ..but it didn't work out so well because I got the wrong answer. Am I thinking about this incorrectly? What other method can I use?

Thanks all for your help.

Diagram seen below:

http://portfolio.iu.edu/whoblitz/rotationalproblem.PNG

 

[Tide]

Have you considered using energy conservation? That would tell you speed versus height which you may be able to integrate and find height versus time.