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PROBLEM 15.33
Two friction wheels A and B are both rotating freely at 300 rpm
counterclockwise when they are brought into contact. After 12 s of
slippage, during which time each wheel has a constant angular acceleration,
wheel B reaches a final angular velocity of 75 rpm counterclockwise.
Determine (a) the angular acceleration of each wheel during the period of
slippage, (b) the time at which the angular velocity of wheel A is equal to
zero.
PROBLEM 15.33 (Continued)
(b) Time when
ω
A is zero.
( )
0
0
AA A
t
ωω α
= +=
( )
00 31.416
3.4034
AA
A
t
ωω
α
−−
= = −
9.23 st=
PROBLEM 15.34
Two friction disks A and B are to be brought into contact without slipping when the
angular velocity of disk A is 240 rpm counterclockwise. Disk A starts from rest at
time t = 0 and is given a constant angular acceleration of magnitude
.
α
Disk B starts
from rest at time t = 2 s and is given a constant clockwise angular acceleration, also
of magnitude
.
α
Determine (a) the required angular acceleration magnitude
,
α
(b) the time at which the contact occurs.
PROBLEM 15.35
Two friction disks A and B are brought into contact when the angular velocity of disk
A is 240 rpm counterclockwise and disk B is at rest. A period of slipping follows and
disk B makes 2 revolutions before reaching its final angular velocity. Assuming that
the angular acceleration of each disk is constant and inversely proportional to the
cube of its radius, determine (a) the angular acceleration of each disk, (b) the time
during which the disks slip.
PROBLEM 15.36*
Steel tape is being wound onto a spool that rotates with a constant angular
velocity
0.
ω
Denoting by r the radius of the spool and tape at any given
time and by b the thickness of the tape, derive an expression for the
acceleration of the tape as it approaches the spool.
PROBLEM 15.37*
In a continuous printing process, paper is drawn into the presses
at a constant speed v. Denoting by r the radius of the paper roll
at any given time and by b the thickness of the paper, derive an
expression for the angular acceleration of the paper roll.
PROBLEM 15.38
An automobile travels to the right at a constant speed of
48 mi/h. If the diameter of a wheel is 22 in., determine the
velocities of Points B, C, D, and E on the rim of the wheel.
PROBLEM 15.39
The motion of rod AB is guided by pins attached at A and B
which slide in the slots shown. At the instant shown,
40
θ
= °
and the pin at B moves upward to the left with a constant
velocity of 6 in./s. Determine (a) the angular velocity of the
rod, (b) the velocity of the pin at end A.
PROBLEM 15.40
A painter is halfway up a 10-m ladder when the bottom starts
sliding out from under him. Knowing that point A has a velocity
vA = 2 m/s directed to the left when θ= 60°, determine (a) the
angular velocity of the ladder, (b) the velocity of the painter.
PROBLEM 15.41
Rod AB can slide freely along the floor and the inclined plane. At
the instant shown the velocity of end A is 1.4 m/s to the left.
Determine (a) the angular velocity of the rod, (b) the velocity of end
B of the rod.
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