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Discussion
The animation shown above demonstrates the kinematics of the motion of the bar/particle/spring system. The bar rotates about its center of mass G. The particle is attached to end B of the bar such that the particle has the same velocity at point B on the bar. The system is released from rest with the bar being horizontal and the spring being unstretched.
You are asked to determine the rotation rate of the bar when the bar reaches the vertical position shown below.
HINT: As always, we should follow the four-step plan for solving this problem.
STEP 1: FBD. We will be using the work/energy equation to determine this angular speed. Based on earlier recommendations, we will make the choice of our system BIG, including the bar, particle and spring.
STEP 2: Kinetics (here, work/energy). The total kinetic energy of the system shown in your FBD above is that of the bar + that of the particle. The center of mass of the bar is a fixed point, making the choice of reference point for KE easy. The KE of the particle is simply 0.5*m*vB2. The spring is initially unstretched, so the spring does not contribute to the PE at position 1. Be sure to identify the datum line for the gravitational potential energy, and use this in writing down this potential.
STEP 3: Kinematics. You need to relate the speed of B to the angular speed of the bar.
STEP 4: Solve