Physics 1 Problem Solutions 116

Physics 1 Problem Solutions 116 - 112 Chapt 12 Rotational...

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112 Chapt. 12 Rotational Dynamics c) Say that r 1 = r + Δ r . What is the rotational inertia of the shell to 1st order in small Δ r . HINT: Using the binomial theorem and drop higher order terms. d) What is the mass the shell to 1st order in Δ r ? e) What is the rotational inertia of a differentially thin hollow shell of mass m and radius r ? 012 qfull 00940 2 3 0 moderate math: perpendicular-axis theorem, etc. 6. Do the following problems. a) The perpendicular-axis theorem applies exactly to infinitely thin planar objects and approximately to just thin planar objects. You have a planar object with area density σ . You choose an origin and define a set of coordinates with the x and y axes in the object plane and the z axis perpendicular to the object plane. Show that I z = I x + I y , where I x , I y , and I z are the rotational inertias about, respectively, the x , y , and z axes. b) The rotational inertia of a infinitely thin, uniform rod about axis through its center and perpendicular to the rod is 1 12 Ma 2 , where M
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