Given The pendulum has a clockwise angular velocity of 3 rad

Given: The pendulum has a clockwise angular velocity of 3 rad/s when e 45e and the external moment of 50 N m as shown in the diagram. Masses: mwhere 15 kg. mras 10 kg. Find: The reaction force vector at the pino and the pendulum angular acceleration vector at this moment in time. Use n-t coordinates. The Plan: Apply the Newton-Euler equations of motion. Notice the reaction force at o can be written STEP1: Determine the location of the COM for the pendulum relative to point o. Label this point G. 0(v. 3) 15(0.7) 100 mm STEP 2: Determine lo, the MMI of the pendulum relative to point O. s (10) (6.6) lo STEP 3: Draw the pendulum FBD and KD using n-t coordinates. The FBD should include the reaction force vector at O,the weight vector at the pendulum COM, and the applied external moment at O. STEP 4: Determine the weight vector, as a function of e in n-t coordinates. Cnn 245. 25 e 0.24.5. 25 e

Solution

Simply stated, the external force is that due to gravitation g

Further the force resolved along the vertical and tangential directions must equal the acclerations along thise direction.

Similarly, the torque due to the force at angle theta wil determine the angular accln.

Thus I theta \" = moment (tangential) + component of weight along tangentX radius

Normal:: resolve weight vector along the support beam and put it equal to centripetal force mR² omega, where m is the Total weight, R the COM