1. The structure shown in the figure consists of a uniform thin ring (hoop) of radius...

 

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1. The structure shown in the figure consists of a uniform thin ring (hoop) of radius r = 0.23 m and mass/m M.082 kg. The ring is free to rotate in a vertical plane about a fixed axis located as shown. An additional mass m2.053 kg is attached to the thin ring such that its center of mass is a distance 2r from the axis. Mass m can be treated as a point mass Your solution must start with basic equations in symbolic form. Don't skip steps. Appropriate units are required for all numerical quantities. (a) What is the total rotational inertia of this structure about the indicated axis? The rotational inertia of a thin ring rotating about its center of mass is mr2, where m is the ring's mass and r is the ring's radius. (b) Starting from rest, the structure rotates from the position shown until the point mass m2 is directly beneath the axis, a total rotation of 180. Assuming there is no friction or air resistance, what is the angular velocity of the structure after the 180 rotation? (c) The torque (due to gravity) acting on the structure is not constant as the structure rotates. What is the maximum gravitational torque? (Hint: consider where in its rotation the torque would be greatest). (d) What is the maximum angular acceleration of the structure during its rotation? 1. The structure shown in the figure consists of a uniform thin ring (hoop) of radius r = 0.23 m and mass/m M.082 kg. The ring is free to rotate in a vertical plane about a fixed axis located as shown. An additional mass m2.053 kg is attached to the thin ring such that its center of mass is a distance 2r from the axis. Mass m can be treated as a point mass Your solution must start with basic equations in symbolic form. Don't skip steps. Appropriate units are required for all numerical quantities. (a) What is the total rotational inertia of this structure about the indicated axis? The rotational inertia of a thin ring rotating about its center of mass is mr2, where m is the ring's mass and r is the ring's radius. (b) Starting from rest, the structure rotates from the position shown until the point mass m2 is directly beneath the axis, a total rotation of 180. Assuming there is no friction or air resistance, what is the angular velocity of the structure after the 180 rotation? (c) The torque (due to gravity) acting on the structure is not constant as the structure rotates. What is the maximum gravitational torque? (Hint: consider where in its rotation the torque would be greatest). (d) What is the maximum angular acceleration of the structure during its rotation?

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a The total rotational inertia of the structure can be calculated by summing the rotational inertia of the ring and the point mass The rotational iner... View the full answer