Consider the system shown below. The disk rolls without slip and has a radius of r...

 

 

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Consider the system shown below. The disk rolls without slip and has a radius of r and a mass of 2m. The pulley is massless and frictionless. The rod is assumed to be rigid, homogeneous, and uniform such that it has a mass of m, a length of 2L, and its center of mass is located at directly at its center (i.e., a distance L from either end). The left end of the rod is constrained to move in the vertical direction only whereas the right end is constrained to move in the horizontal direction only. As such, there is a kinematic constraint between x and p as well as y and o (i.e., you can express x and y in terms of o). An external, vertical force, F(t), is applied to left end of the rod. Gravity is included. Determine the equations of motion in terms of 0(t) and ø(t). You will need to express x(t) and y(t) in terms of L and o(t). Determine the total energy at an arbitrary time assuming that the system begins with zero initial energy in terms of 0(t) and o(t). Pro(t) 2rolt) 2m, 0(t) x(t) $(t) www m L Consider the system shown below. The disk rolls without slip and has a radius of r and a mass of 2m. The pulley is massless and frictionless. The rod is assumed to be rigid, homogeneous, and uniform such that it has a mass of m, a length of 2L, and its center of mass is located at directly at its center (i.e., a distance L from either end). The left end of the rod is constrained to move in the vertical direction only whereas the right end is constrained to move in the horizontal direction only. As such, there is a kinematic constraint between x and p as well as y and o (i.e., you can express x and y in terms of o). An external, vertical force, F(t), is applied to left end of the rod. Gravity is included. Determine the equations of motion in terms of 0(t) and ø(t). You will need to express x(t) and y(t) in terms of L and o(t). Determine the total energy at an arbitrary time assuming that the system begins with zero initial energy in terms of 0(t) and o(t). Pro(t) 2rolt) 2m, 0(t) x(t) $(t) www m L