In the days of wooden ships and iron men, a variety of objects were fired from...

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In the days of wooden ships and iron men, a variety of objects were fired from cannons during sea battles, including metal barbells. Let's analyze the linear and angular momentum of an asymmetric barbell comprising a ball with mass and a ball with mass 2 separated by a bar with length 32, hurtling through the air and tumbling along the way. boon Y close up: 2 We'll assume that the bar between the balls is effectively massless, so that the barbell's center of mass C is a distance 1 from the center of the larger ball and a distance 2 from the center of the smaller ball, and we'll assume that each ball can be treated as a point mass. Let O denote the origin of the inertial coordinate system shown and let x + y be the position of C relative to O. Let O represent the angle shown, and assume that x, y, and 0 are all changing with time as the barbell flies through the air. Let gravitational potential energy equal zero at O. Noting that the total linear momentum, angular momentum, kinetic energy, or potential energy in a system can be obtained by summing the contributions of the system's individual components, compute 1. the barbell's total linear momentum; 2. the barbell's total angular momentum with respect to O; 3. the barbell's total angular momentum with respect to C; 4. the barbell's total kinetic energy; 5. the barbell's total potential energy. Suppose that the barbell were replaced by a single ball with mass 3 at the point C. Which of the quantities computed above would remain the same in general? Which would remain the same only in the special case in which = 0? In the days of wooden ships and iron men, a variety of objects were fired from cannons during sea battles, including metal barbells. Let's analyze the linear and angular momentum of an asymmetric barbell comprising a ball with mass and a ball with mass 2 separated by a bar with length 32, hurtling through the air and tumbling along the way. boon Y close up: 2 We'll assume that the bar between the balls is effectively massless, so that the barbell's center of mass C is a distance 1 from the center of the larger ball and a distance 2 from the center of the smaller ball, and we'll assume that each ball can be treated as a point mass. Let O denote the origin of the inertial coordinate system shown and let x + y be the position of C relative to O. Let O represent the angle shown, and assume that x, y, and 0 are all changing with time as the barbell flies through the air. Let gravitational potential energy equal zero at O. Noting that the total linear momentum, angular momentum, kinetic energy, or potential energy in a system can be obtained by summing the contributions of the system's individual components, compute 1. the barbell's total linear momentum; 2. the barbell's total angular momentum with respect to O; 3. the barbell's total angular momentum with respect to C; 4. the barbell's total kinetic energy; 5. the barbell's total potential energy. Suppose that the barbell were replaced by a single ball with mass 3 at the point C. Which of the quantities computed above would remain the same in general? Which would remain the same only in the special case in which = 0?