Problem 5/2 Page 333, Engineering Mechanics - Dynamics, Meriam and Kraige, 4th Edition
Given: T shaped body rotating about point O with known angular velocity and angular acceleration.
Find: The velocity and acceleration of several points on the body.
w = 3 rad/s k
a = -14 rad/s2 k
rA/O = -0.4 m n
rB/O = -0.4 m n + 0.1 m t
t, n, k form a right handed set of mutually perpendicular axes.
vA = vO + w
X rA/O
= 0 + 3 rad/s k X -0.4 m n
= 1.2 m/s t
vB = vO + w
X rB/O
= 0 + 3 rad/s k X (-0.4 m n
+ 0.1 m t ) = 1.2 m/s t + 0.3 m/s n
aA = aO + w
X ( w X rA/O )
+ a X rA/O
= 0 + 3 rad/s k X ( 3 rad/s
k X -0.4 m n ) - 14 rad/s2 k X -0.4
m n
= 3 rad/s k X 1.2 m/s t -5.6
m/s2 t
= 3.6 m/s2 n - 5.6 m/s2
t
aB = aO + w
X ( w X rB/O )
+ a X rB/O
= 0 + 3 rad/s k X ( 3 rad/s
k X ( -0.4 m n + 0.1 m t) ) - 14 rad/s2
k X (-0.4 m n + 0.1 m t )
= 3 rad/s k X ( 1.2 m/s t +
0.3 m/s n ) -5.6 m/s2 t - 1.4 m/s2
n
= 3.6 m/s2 n - 0.9 m/s2
t - 5.6 m/s2 t - 1.4 m/s2 n
= 2.2 m/s2 n - 6.5 m/s2
t