(a) A uniform, thin rod of length L and mass M has a frictionlesspivot at one end. Starting from the definition of moment of inertiaas I = | r dm, show that the rod has a moment of inertia given byI3(b) The rod is initially vertical (with the pivot at the bottom) andfalls under gravity. By considering that gravity acts on the rod'scenter of mass, find the torque acting on the rod when it is at anangle 0 to the vertical, and hence show that the angular accelerationis given by3g sin 02Lwhere g is the acceleration due to gravity.(c) Sketch a as a function of 0.(d) Hence find the linear acceleration of the center of mass whenthe rod is horizontal. Show also that when the rod is horizontal thelinear acceleration of the tip of the rod is greater than that of anobject in free-fall.(e) Make a rough sketch of the distance travelled by the tip as afunction of time as the rod moves through one full revolution.

(a) A uniform, thin rod of length L and mass M has a frictionless pivot at one end. Starting from the definition of moment of inertia as I = | r² dm, show that the rod has a moment of inertia given by 1 -ML². 3 (b) The rod is initially vertical (with the pivot at the bottom) and falls under gravity. By considering that gravity acts on the rod's center of mass, find the torque acting on the rod when it is at an angle 0 to the vertical, and hence show that the angular acceleration

(a) A uniform, thin rod of length L and mass M has a frictionless pivot at one end. Starting from the definition of moment of inertia as I = | r² dm, show that the rod has a moment of inertia given by 1 -ML². 3 (b) The rod is initially vertical (with the pivot at the bottom) and falls under gravity. By considering that gravity acts on the rod's center of mass, find the torque acting on the rod when it is at an angle 0 to the vertical, and hence show that the angular acceleration

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter10: Rotational Motion

Section: Chapter Questions

Problem 10P: A wheel 2.00 m in diameter lies in a vertical plane and rotates about its central axis with a...

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