physics
posted by tara .
A 3.28kg bucket is attached to a diskshaped pulley of radius 0.108 m and mass 0.727 kg.
(a) If the bucket is allowed to fall, what is its linear acceleration?
(b) What is the angular acceleration of the pulley?
(c) How far does the bucket drop in 1.65 s?

T = tension in line
free body of bucket (Positive is down):
mg  T = m a
free body of pulley:
acceleration a = angular acceleration alpha * r
alpha = moment/I
I = (1/2) m r^2 =
moment = T r
so
alpha = 2 T r/ m r^2 = 2 T/m r
a = alpha r = 2 T/m
therefore
mg  T = m a but a = 2 T/m
so
m g  T = 2T
T = m g/3
now go back and get a and alpha etc