Physics rotation question?

Question

A 8cm radius disk with a rotational inertia of .12kgm^2 is free to rotate on a horizontal axis. A string is fastened to the surface of the disk and a 10kg mass hangs from the other end. The mass is raised by using a crank to apply a 9Nm torque to the disk. Find the acceleration of the mass.

Answer 1

The torque of the rising mass is the tension in the string times the radius of the disk:
First solve for the tension in the string:
T-10*9.81=10*a
where T is the tension and a is the acceleration upward
T=10*(9.81+a)

The torque on from the rising mass is
T*8/100=8*(9.81+a)/10

Therefore, the net torque is
9-8*(9.81+a)/10
this is equal to the inertia times α, and α=a/r
so
9-8*(9.81+a)/10=0.12*a*100/8

solve for a

90-8*(9.81+a)=120*a/8
720-64*(9.81+a)=120*a
92.16=184*a
a=0.50 m/s^2

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