Homework H.5.D
Given: An inextensible cable is wrapped around the inner radius of a solid, stepped drum (having
a mass of $m$, inner radius $r$, outer radius $R$ and radius of gyration about its center O of $k_O$). One
end of the cable is attached to ground, with a vertical force $F$ acting at the free end of the cable.
A second inextensible cable is wrapped around the outer radius of the drum with block B (of mass
$m$) attached at its free end. Neither cable slips on the drum as the system moves. The system is
released from rest.
Find: On release:
(a) Determine the angular acceleration of the drum.
(b) Determine the acceleration of block B.
HINT: Since the drum does not slip on the cables, point C is the instant center for the drum.
F
r
C
O
R
m
m
B
g
Use the following parameters in your analysis: $m = 8$ kg, $R = 0.5$ m, $r = 0.25$ m, $k_O = 0.3$ m and
$F = 20$ N.
