Problem: A massless string is wrapped around a solid cylinder as shown in the diagram at the right. A block of mass m = 2.0 kg hangs from the string. When released, the block falls a distance of 82 cm in 2.0 s. Starting with a free-body diagram, calculate the mass of the cylinder.
d = Vot + 0.5at^2
Tension = ma - mg
Torque = (I)(alpha) = F(r)
The Attempt at a Solution
Conceptually, I figure I need to find the force being exerted on the wheel, and the acceleration. That will leave nothing but the mass to be determined. But the fact that it's rotational, throws a wrench into it, especially since no radius is provided.
using d = Vot + 0.5at^2 we get a = 0.41 m/s^2 for the block.
Tension is therefore, 18.78 N in the opposite direction of the block's movement and is the force being exerted on the wheel (I think).
Torque = 18.78(r) = 0.5Mr^2(a/r)
If my approach is right, I need M, but r is in the way. What to do?