Question

QUESTIONS (Q.1. 35 pts) The rectangular plate shown rotates at the constant rate 02 =8 rad/s with respect to arm AE, which itself rotates at the constant rate 0,=5 rad/s about the Z axis. For the position shown, determine the velocity and acceleration of point C. 120 mm 150 AM G Z 150 mm

Answer 1

solutions With origin at re= (0.150 m)j + (0.12 m )k The frame AXYZ rotates about the y-axis with constant angular velocity 2= wik. R = (5 rad/s) k wg = wzi = (Brad's) i Motion of coinciding point c' Vcl = rare = 5kx (0,150 j +0.12 k) Vc = -(0.75 mls); ac = 2xrctravel = 0+ 5kx(-0.451) ac' = -(3.75 m/s2); The motion relative to the frame. VC/F=Wzx8c 8ix (0.150j +0.12k) Volf = -(0,96 m/s) j+(1.2m/s) k acle = dq XYC + W₂ X Velf 0+8ix (-0.96; +12k) --9.6 m/s2);-4.68 m/s2) * And the velocity of point c. Vc = vci AVCF acf

ace actacleta RAVCIF Ve=-{0.75 mls) i-(0.96 m/s)j + (1.2 m/s) k By coriolis acceleration 22x Volf 2 1 X VCF = (2)(5K) * (-0.963 +1·2k) = (9.6 m/s²); Then the Acceleration of point c. ąc = (9.6 m/s2); - (13.35 m/s2); - (7.68 m/s 2)k