The figure shows a rigid assembly of a thin hoop (of mass m = 0.24 kg and radius R = 0.16 m) and a thin radial rod (of length L = 2R and also of mass m = 0.24 kg). The assembly is upright, but we nudge it so that it rotates around a horizontal axis in the plane of the rod and hoop, through the lower end of the rod. Assuming that the energy given to the assembly in the nudge is negligible, what is the assembly's angular speed about the rotation axis when it passes through the upside-down (inverted) orientation? O Rod Hoop Rotation axis
The figure shows a rigid assembly of a thin hoop (of mass m = 0.24 kg and radius R = 0.16 m) and a thin radial rod (of length L = 2R and also of mass m = 0.24 kg). The assembly is upright, but we nudge it so that it rotates around a horizontal axis in the plane of the rod and hoop, through the lower end of the rod. Assuming that the energy given to the assembly in the nudge is negligible, what is the assembly's angular speed about the rotation axis when it passes through the upside-down (inverted) orientation? O Rod Hoop Rotation axis
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Step 1: Define the law of conservation of energy:
VIEWStep 2: Draw a diagram of the given problem.
VIEWStep 3: Find the expression for the initial energy of the system:
VIEWStep 4: Find the expression for the final kinetic energy of the system:
VIEWStep 5: Find the expression for the final energy of the system:
VIEWStep 6: Calculate the final angular speed of the system.
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