A disk with a mass of 29 kg and a radius of 31 cm is mounted on a frictionless horizontal axle. A string is wound many times around the disk and then attached to a 70-kg block, as shown in the figure. Find the acceleration of the block, assuming that the string does not slip.

Answer 1

R = .31 m
Tension in string = T
torque = T * R = I alpha
so T = (I/R)alpha
but a = alpha * R
so
T = (I/R)(a/R) = (I/R^2) a

force on block = m a = m g -T
ma = mg - (I/R^2) a
but I = (1/2) mdisk R^2
m a = m g - (Mdisk/2) a
70 a = 70*9.8 - 14.5 a
solve for a