Question

15.123.) The disk shown has a constant angular velocity of 500 rpm counterclockwise. Knowing that rod BD is 10 in. long, determine the acceleration of collar D when θ=55°.

15.123 The disk shown has a constant angular velocity of 500 rpm counter- clockwise. Knowing that rod BD is 10 in. long, determine the accel- eration of collar D when (a) 90°, (b) 180 in Fig. P15.12 6 in Fig. P15.123

Answer 1

Angular velocity w_disk = 500 rpm = 500 times 2 pi/60 rad/s = 52.36 rad/s length of rod BD = 10 inch doublerightarrow 254mm length of AB = 2 inch doublerightarrow 50.8mm doublerightarrow 0.0508m For theta = 90 degree consider the disk d_B = (AB)w^2_disk = (0.05) (52.36)^2 = 137.08 m/s^2 rightarrow now consider the rod BD we know, V_B and V_D are parallel so, w_BD = 0 now, w_BD = 0 now, sin beta = 101.6 mm/254 mm beta = 23.58 degree we know that a_D = a_B + a_D/B [a_D updownarrow] = [a_B rightarrow] + [0.254 alpha < beta] a_D = a_B tan beta a_D = 137.08 times tan 23.58 degree a_D = 59.83 m/s^2 \r\n (b) Now for theta = 180 degree consider the disk V_B = (AB) w_disk V_B = 0.05 times 52.36 = 2.168 m/s rightarrow a_B = (AB) w^2_disk = 0.05 times (52.36)^2 = 137.08 m/s^2 rightarrow Now consider the rod BD BD = 254 mm