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PROBLEM 16.93
Show that in the case of an unbalanced disk, the equation derived in Problem 16.92 is valid only when the
mass center G, the geometric center O, and the instantaneous center C happen to lie in a straight line.
PROBLEM 16.94
A wheel of radius r and centroidal radius of gyration
k
is released from rest on
the incline and rolls without sliding. Derive an expression for the acceleration of
the center of the wheel in terms of r,
,k
,
β
and g.
PROBLEM 16.95
A homogeneous sphere S, a uniform cylinder C, and a thin pipe P
are in contact when they are released from rest on the incline
shown. Knowing that all three objects roll without slipping,
determine, after 4 s of motion, the clear distance between (a) the
pipe and the cylinder, (b) the cylinder and the sphere.
PROBLEM 16.95 (Continued)
(b) Between sphere and cylinder.
PROBLEM 16.96
A 40-kg flywheel of radius R = 0.5 m is rigidly attached to a shaft of radius
r = 0.05 m that can roll along parallel rails. A cord is attached as shown and
pulled with a force P of magnitude 150 N. Knowing the centroidal radius of
gyration is
0.4 m,k=
determine (a) the angular acceleration of the
flywheel, (b) the velocity of the center of gravity after 5 s.
PROBLEM 16.96 (Continued)
(b) Velocity of center of gravity after 5 s.
22
(0.05 m)(11.911rad/s ) 0.59555 m/sar
a
= = =
2
PROBLEM 16.97
A 40-kg flywheel of radius R = 0.5 m is rigidly attached to a shaft of radius
r = 0.05 m that can roll along parallel rails. A cord is attached as shown and
pulled with a force P. Knowing the centroidal radius of gyration is
0.4 mk=
and the coefficient of static friction is
0.4,
s
µ
=
determine the
largest magnitude of force P for which no slipping will occur.
PROBLEM 16.97 (Continued)
Let C be the contact point between the flywheel and the rails.
PROBLEM 16.98
A drum of 60-mm radius is attached to a disk of 120-mm radius. The
disk and drum have a total mass of 6 kg and a combined radius of
gyration of 90 mm. A cord is attached as shown and pulled with a force
P of magnitude 20 N. Knowing that the disk rolls without sliding,
determine (a) the angular acceleration of the disk and the acceleration of
G, (b) the minimum value of the coefficient of static friction compatible
with this motion.
PROBLEM 16.99
A drum of 60-mm radius is attached to a disk of 120-mm radius. The
disk and drum have a total mass of 6 kg and a combined radius of
gyration of 90 mm. A cord is attached as shown and pulled with a force P
of magnitude 20 N. Knowing that the disk rolls without sliding,
determine (a) the angular acceleration of the disk and the acceleration of
G, (b) the minimum value of the coefficient of static friction compatible
with this motion.
