Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)
12th Edition
ISBN: 9781259587399
Author: Eugene Hecht
Publisher: McGraw-Hill Education
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Chapter 10, Problem 37SP

A uniform homogeneous rod of length L and mass m is in a horizontal plane. It hangs from an essentially massless wire of length L attached to the rod’s center of mass at one end and to a ceiling hook at the other end. Determine the rod’s moment of inertia about the hook. [Hint: Use the Parallel-Axis Theorem and Fig. 10-1, and look at the previous problem.]

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A rigid body consists of 12 identical thin rods of length a, forming the edges of a cube. Each of the rods has mass m and a uniform mass density. Calculate the moment of inertia tensor of the body. [Expect to use about half a page to answer the question.]
A uniform rod of mass m, = 153 g and length L = 100.0 cm is attached to the wall with a pin as shown. Cords are attached to the rod at the r, = 10.0 cm and r, = 90.0 cm mark, passed over pulleys, and masses of m, = 286 g and m, = 187 g are attached. Your TA asks you to determine the following. (a) The position r, on the rod where you would suspend mass m3 200 g in order to balance the rod and keep it horizontal if released from a horizontal position. In addition, for this case, %3D what force (magnitude and direction) does the pin exert on the rod? Use standard angle notation to determine the direction of the force the pin exerts on the rod. Express the direction of the force the pin exerts on the rod as the angle 0F, measured with respect to the positive x-axis (counterclockwise is positive and clockwise is negative). r3 0.602 m 0.49 F. See if you can write a condition for rotational equilibrium statement that will allow you to determine the position on the rod where we need to…
Problem 1 (i) Show that all three principal moments of inertia of a solid regular dodecahedron are equal. Hint: you do not need to compute their values. (ii) A rigid body consists of 12 identical thin rods of length a, forming the edges of a cube. Each of the rods has mass m and a uniform mass density. Calculate the moment of inertia tensor of the body.

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Schaum's Outline of College Physics, Twelfth Edition (Schaum's Outlines)

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