ME 232 Homework Problems

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