o AT&T; LTE 2:11 PM webassign.net A uniform rod of length L = 1.5 m and massM-2.
ID: 1784589 • Letter: O
Question
o AT&T; LTE 2:11 PM webassign.net A uniform rod of length L = 1.5 m and massM-2.8 kg is attached at one end to a frictionless pivot and is free to rotate about the pivot in the vertical plane as in the figure. The rod is released from rest in the horizontal position. What are the initial angular initial translational acceleration of its right end? Conceptualize Imagine what happens to the rod in the figure when it is released. It rotates clockwise around the pivot at the left end. Categorize The rod is categorized as a rigid object under a net torque. The torque is due only to the gravitational force on the rod if the rotation axis is chosen to pass through the pivot in the figure. We cannot categorize the rod as a rigid object under constant angular acceleration because the torque exerted on the rod and therefore the angular acceleration of the rod vary with its angular position. Analyze The only force contributing to the torque about an axis through the pivot is the gravitational force exerted on the rod. (The force exerted by the pivot on the rod has zero torque about the pivot because its moment arm is zero.) To compute the torque on the rod, we assume the gravitational force acts at the center of mass of the rod as shown in the et estermal torgue du graveational force about an axis through ne angu Finalize These values are the initial values of the angular and translational accelerations. Once the rod begins to rotate, the gravitational force is no longer perpendicular to the rod and the values of the two accelerations decrease, going to zero at the moment the rod passes through the vertical orientation.Explanation / Answer
from conservation of energy threorem
Potential energy = kinetic energy
mgh = 0.5 Iw2
mg(L/2) cos28 = 0.5 (1/3) m L2w2
3g cos28 = L w2
w2 = 3 x 9.8 x0.8829 /0.82 = 31.655
angular velocity w = sq.root of 31.655 = 5.62 rad/s
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.