Movimento relativo com eixos em rotação

with a constant counterclockwise angular velocity V, determine the
acceleration of each pin. u
Fig. P15.156 and P15.157
w
P
q
A
15.159 Solve Prob. 15.158,
assuming
that the plate rotates about O with
r
500 mm
a constant clockwise angular velocity V.
P2
DepartamentodeEngenhariaMecânica u
ÁreaCientíficadeMecânicadosMeiosSólidos Fig. P15.172
15.160 At the instant
shown
the length of the boom AB is being decreased
15.173
Pin
P
slides
in aof
circular
slot and
cut inthe
the boom
plate shown
at a constant
at the constant rate
0.2 m/s
is being
lowered at the
r
relative speed u 5 90 mm/s. Knowing that at the instant shown
constanttherate
of
0.08
rad/s.
Determine
(a)
the
velocity
of point B,
P3 u
plate rotates clockwise about A at the constant rate v 5 3 rad/s,
MecânicaAplicada
(b) the determine
acceleration
of point B.
the acceleration
of the pin if it is located at (a) point A,
r
P1
O
u
r
Cap.151-Movimentorelativocomeixosemrotação
r
(b) point B, (c) point C.
P4
u
Problema15.160
C
u
100 mm
P
B
Fig. P15.158
6 m𝑚 5,4
B
No instante mostrado na figura, o comprimento da lança𝐴𝐵está
A
sendo diminuído a uma taxa constante de0,18 𝑚/𝑠e a lança está
q = 30!
w
sendobaixadaaumataxaconstantede0,08 𝑟𝑎𝑑/𝑠.Determine:
A
Fig. P15.173 and P15.174
(a) avelocidadedoponto𝐵;
15.174 Pin P slides in a circular slot cut in the plate shown at a constant
(b) aaceleraçãodoponto𝐵.
relative speed u 5 90 mm/s. Knowing that at the instant shown
the angular velocity V of the plate is 3 rad/s clockwise and is
decreasing at the rate of 5 rad/s2, determine the acceleration of the
pin if it is located at (a) point A, (b) point B, (c) point C.
rod attached
Knowing that at the instant shown the
P15.160
P15.161 angular velocity VB
Fig.with
at B rotates
a constantand
counterclockwise
of 6 rad/s,
determine the angular velocity and angular acceleration
of the rod attached at A.
15.175 and 15.176
Problema15.175
y
5 in.
0.4 m
0.4 m
15.161 At the instant shown the length of the boom AB is being increased
bee29400_ch15_0914-1023.indd
982a barra
12/14/08
9:27:50em
AM B
user-s172
/Volumes/204/MHDQ077/
Sabendo que
no instante mostrado naPage
figura,
articulada
F
at the constant
rate of 0.2 m/s and the boom is being lowered at the
A
B
A
constant
30! Determine (a) the velocity of point B,
C
A
B constante
gira no sentido anti-horário com
velocidade
angular
de rate of 0.08 rad/s.
x
30!
(b) the acceleration of point B.
z
𝜔 = 6 𝑟𝑎𝑑/𝑠, determine
a velocidade angular e a aceleração angular
12 in.
15.162 and 15.163
The sleeve BC is welded to an arm that rotates
D
about A with a constant angular velocity
V. In the position shown
D
Kinematics
of
Rigid
Bodies
B
15.172
The
collar
P
slides
outward
at
a
constant
relative
speed
along
rod
DF
is
being
moved
to
the
left
at
a constant
speed
u 5u 16
in./s
982
rod AB,
which
rotates
with
a constant
angular
relative
to the
sleeve.
Forcounterclockwise
the given angular
velocity
V, determine
Fig. P15.176
12 in. Fig. P15.175
20(a)
rpm.
Knowing
thatofrthe
5 250
whenDF
u5
0 and
of
the velocity
acceleration
of point
D, (b)
pointmm
of rod
that
coinD
u
that
thepoint
reaches B when u 5 90°, determine the magnitude
Problema15.170
collarE.
cides
with
of15.162
the acceleration
the collar
P just as it reaches B.
i.
V 5 (3 ofrad/s)
Ocolar𝑃deslizaparaforacomumavelocidaderelativaconstante𝑢ao
15.163 V 5 (3 rad/s) j.
Fig. P15.162 and P15.163
B
dabarraarticuladaemA.
E
longo da barra𝐴𝐵 , que roda no sentido𝑎𝑛𝑡𝑖 − ℎ𝑜𝑟á𝑟𝑖𝑜 com uma
u
w
velocidadeangularconstantede20 𝑟𝑝𝑚.
Sabendo que𝑟 = 25𝑐𝑚 quando𝜃 = 0°e que o colar P chega a B
P
q
A
r
500 mm
quando𝜃 = 90°,determineaintensidadedaaceleraçãodocolar𝑃no
momentoexatoemqueeleatingeoponto𝐵.
Fig. P15.172
15.173 Pin P slides in a circular slot cut in the plate shown at a constant
relative speed u 5 90 mm/s. Knowing that at the instant shown
the plate rotates clockwise about A at the constant rate v 5 3 rad/s,
determine the acceleration of the pin if it is located at (a) point A,
(b) point B, (c) point C.
C
u
P
100 mm
B
A
w
Fig. P15.173 and P15.174
15.174 Pin P slides in a circular slot cut in the plate shown at a constant
relative speed u 5 90 mm/s. Knowing that at the instant shown
the angular velocity V of the plate is 3 rad/s clockwise and is
1Osproblemasapresentadosreferem-seaolivro“MecânicaVetorialparaEngenheiros–Dinâmica,FerdinandP.Beer,E.Russell
decreasing at the rate of 5 rad/s2, determine the acceleration of the
JohnstonJr.,WilliamE.Clausen,7ªEdMcGraw-Hill”
pin if it is located at (a) point A, (b) point B, (c) point C.
RMM–2015/16
15.175 and 15.176
Knowing that at the instant shown the rod attached
at B rotates with a constant counterclockwise angular velocity VB
of 6 rad/s, determine the angular velocity and angular acceleration
of the rod attached at A.