A square plate of mass 12 kg and side length a = 0.5 m has an angular velocity o

Question

A square plate of mass 12 kg and side length a = 0.5 m has an angular velocity omega 1 = 8 rad/s while rotating on a smooth surface. Determine its new angular velocity just after its corner strikes and hooks onto the peg and the plate starts to rotate about P without rebounding. (Moment of inertia about the vertical axis through the middle of the plate is (l/12)*m*(a2 + a2)) At the instant shown, the tower crane is rotating about the z axis with an angular velocity omega 1 = 0.25 rad/s, which is increasing at 0.6 rad/s2. The boom OB is rotating downward with an angular velocity omega 2 = 0.4 rad/s, which is increasing at 0.8 rad/s2. Determine the total angular velocity and angular acceleration of the boom Calculate the velocity of point B located at the top of the boom. At the instant shown, the base of the robotic arm is turning about the z axis with an angular velocity of omega 1 = 4 rad/s, which is increasing at = 3 rad/s2. Also, the boom segment BC is rotating at omega BC = 8 rad/s, which is increasing at = 2 rad/s2. The gripper is retracting at a constant rate vC = l m/s. Calculate the velocity of point C. (extra) Find the acceleration of point C.

Explanation / Answer

5. 2 rad/sec

6. Angular speed=0.472rad/sec

Angular acceleration= 1 rad/sec2

Velocity of point B=16.76 ft/sec

7. Angular speed=8.944rad/sec

Angular acceleration=3.606 rad/sec2

Velocity of point B=6.26 m/sec

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