Help! I am stuck on this problem and don\'t think I am doing it right. Any help

Question

Help! I am stuck on this problem and don't think I am doing it right. Any help would be greatly appreciated!

All conditions of the previous problem remain the same, except now, rather than rotating about a fixed center, the disk rolls without slipping on the horizontal surface. If the disk has a clockwise angular velocity of 20 rad/s and a counterclockwise angular acceleration of 5 rad/s2, determine the velocity and acceleration of pin A relative to the slot-member BC and the angular velocity and angular acceleration of BC. The value of r is 200 mm Neglect the distance from the center of pin A to the edge of the disk.

Explanation / Answer

rw = 0.2*20 = 4m/s, linear speed, v = 4m/s

OA/sin(ABO) = OB/sin(120-ABO)

3sin(ABO) = sin(120 - ABO) = sin(60+ABO)

3sin(ABO) = 0.866*cos(ABO) + 0.5sin(ABO)

2.5sin(ABO) = 0.866cos(ABO)

tan(ABO) = 0.3464

angle ABO = 19.106 deg

velocity of A = v+rw

velocity of A in BC direction = v*cos(19.106) + rw*cos(30-19.106) = 7.707m/s

AB/sin60 = OA/sin19.106

AB = 0.525m

Speed of A perpendicular to BC = vsin19.106 - rw*sin(30-19.106) = 0.553m/s

angular speed of BC = 0.553/AB = 0.553/0.525 = 1.053

similar calculation for acceleration of A and angular acceleration of BC,

put a instead of v and r*alpha instead of rw

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