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PROBLEM 17.76 (Continued)
Moments about B:
2
(4 )
1
4( ) (4 )
12
ABC
ABC
Mt Qt r I
Mt Qt r m r
4
2
4(9)
3
A
BC C
M
trm m
(3)
Couple M.
Data:
2.5 s
2ft
32.2 ft/s
t
r
2.5 M 0.76607
0.3064 lb ftM
0.306 lb ftM
PROBLEM 17.77
A sphere of radius r and mass m is projected along a rough horizontal surface
with the initial velocities shown. If the final velocity of the sphere is to be zero,
express (a) the required magnitude of
0
in terms of v
0
and r, (b) the time
required for the sphere to come to rest in terms of v
0
and coefficient of kinetic
friction
.
k
PROBLEM 17.78
A bowler projects an 8.5-in.-diameter ball weighing 16 lb along an alley with a forward
velocity v0 of 25 ft/s and a backspin
0 of 9 rad/s. Knowing that the coefficient of
kinetic friction between the ball and the alley is 0.10, determine (a) the time t1 at which
the ball will start rolling without sliding, (b) the speed of the ball at time t1.
PROBLEM 17.78 (Continued)
(a) Time t when slipping stops.
tt
PROBLEM 17.79
A semicircular panel of radius r is attached with hinges to a circular plate of radius
r and initially held in the vertical position as shown. The plate and the panel are
made of the same material and have the same thickness. Knowing that the entire
assembly is rotating freely with an initial angular velocity 0,
determine the
angular velocity of the assembly after the panel has been released and comes to rest
against the plate.
PROBLEM 17.80
A satellite has a total weight (on Earth) of 250 lbs, and each of the solar panels
weighs 15 lbs. The body of the satellite has mass moment of inertia about the z-
axis of 6 slug-ft2, and the panels can be modeled as flat plates. The satellite
spins with a rate of 10 rpm about the z-axis when the solar panels are
positioned in the xy plane. Determine the spin rate about z after a motor on the
satellite has rotated both panels to be positioned in the yz plane (as shown in the
figure).
PROBLEM 17.81
Two 10-lb disks and a small motor are mounted on a 15-lb rectangular
platform which is free to rotate about a central vertical spindle. The
normal operating speed of the motor is 180 rpm. If the motor is started
when the system is at rest, determine the angular velocity of all elements
of the system after the motor has attained its normal operating speed.
Neglect the mass of the motor and of the belt.
1
12
2
PROBLEM 17.81 (Continued)
Moments about O:
00 P P AAOA A A BBOB B B
ImvlImvlI
1044 1044
Angular velocities. 159.1 rpm
A
PROBLEM 17.82
A 3-kg rod of length 800 mm can slide freely in the 240-mm cylinder
DE, which in turn can rotate freely in a horizontal plane. In the
position shown the assembly is rotating with an angular velocity of
magnitude 40 rad/s
and end B of the rod is moving toward the
cylinder at a speed of 75 mm/s relative to the cylinder. Knowing that
the centroidal mass moment of inertia of the cylinder about a vertical
axis is
2
0.025 kg m
and neglecting the effect of friction, determine
the angular velocity of the assembly as end B of the rod strikes end E
of the cylinder.
Copyright © McGraw-Hill Education. Permission required for reproduction or display.
PROBLEM 17.83
A 1.6-kg tube AB can slide freely on rod DE, which in turn can rotate freely in a
horizontal plane. Initially the assembly is rotating with an angular velocity
5 rad/s
and the tube is held in position by a cord. The moment of inertia of
the rod and bracket about the vertical axis of rotation is
2
0.30 kg m
and the
centroidal moment of inertia of the tube about a vertical axis is
2
0.0025 kg m .
If
the cord suddenly breaks, determine (a) the angular velocity of the assembly after
the tube has moved to end E, (b) the energy lost during the plastic impact at E.
