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PROBLEM 15.249
Two blocks and a pulley are connected by inextensible cords as
shown. The relative velocity of block A with respect to block B
is 2.5 ft/s to the left at time t = 0 and 1.25 ft/s to the left when
t = 0.25 s. Knowing that the angular acceleration of the pulley
is constant, find (a) the relative acceleration of block A with
respect to block B, (b) the distance block A moves relative to
block B during the interval
0 0.25t≤≤
s.
PROBLEM 15.250
A baseball pitching machine is designed to deliver a
baseball with a ball speed of 70 mph and a ball rotation
of 300 rpm clockwise. Knowing that there is no
slipping between the wheels and the baseball during the
ball launch, determine the angular velocities of wheels
A and B.
PROBLEM 15.251
Knowing that inner gear A is stationary and outer gear C starts from rest
and has a constant angular acceleration of 4 rad/s2 clockwise, determine
at t = 5 s (a) the angular velocity of arm AB, (b) the angular velocity of
gear B, (c) the acceleration of the point on gear B that is in contact with
gear A.
PROBLEM 15.251 (Continued)
Calculate tangential accelerations:
1
2
22
() 0
( ) ( ) (200 mm)(4 rad/s )
t
t Ct C
a
a ar
α
=
= = =
2
PROBLEM 15.252
Knowing that at the instant shown bar AB has an angular velocity of
10 rad/s clockwise and it is slowing down at a rate of 2 rad/s2,
determine the angular accelerations of bar BD and bar DE.
PROBLEM 15.252 (Continued)
2
//
2
0.4 20 ( 0.6 0.25 ) (8) ( 0.6 0.25 )
D B BD D B BD D B
BD
ω
α
=+×−
= ++ ×−− − −−
aaαr r
ijk ij ij
BD DE
2
3 180 736.8 rad/s
DE BD
αα
= −=
Angular acceleration:
2
306 rad/s
BD
=α
2
PROBLEM 15.253
Knowing that at the instant shown rod AB has zero angular
acceleration and an angular velocity of 15 rad/s
counterclockwise, determine (a) the angular acceleration of
arm DE, (b) the acceleration of Point D.
PROBLEM 15.253 (Continued)
()a
:
5 sin 1125cos 1125cos 1440
DE
αβ β β
+ =−−
2
2
PROBLEM 15.254
Rod AB is attached to a collar at A and is fitted with a
wheel at B that has a radius r = 15 mm. Knowing that
when
θ
= 60° the collar has velocity of 250 mm/s
upward and the speed of the collar is decreasing at a
rate of 150 mm/s2, determine (a) the angular
acceleration of rod AB, (b) the angular acceleration of
the wheel.
PROBLEM 15.254 (Continued)
Resolve into components:
i:
cos 0.1
B AB
v
βω
= +
(1)
