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You want to find the moment of inertia of a complicated
Chapter 14, Problem 43E(choose chapter or problem)
You want to find the moment of inertia of a complicated machine part about an axis through its center of mass. You suspend it from a wire along this axis. The wire has a torsion constant of 0.450 \(\mathrm{N} \cdot \mathrm{m} / \mathrm{rad}\). You twist the part a small amount about this axis and let it go, timing 125 oscillations in 265 s. What is its moment of inertia?
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QUESTION:
You want to find the moment of inertia of a complicated machine part about an axis through its center of mass. You suspend it from a wire along this axis. The wire has a torsion constant of 0.450 \(\mathrm{N} \cdot \mathrm{m} / \mathrm{rad}\). You twist the part a small amount about this axis and let it go, timing 125 oscillations in 265 s. What is its moment of inertia?
ANSWER:Solution 43E The angular displacement of balance wheel of a watch which is vibrating with an angular amplitude ,angular frequency and phase angle =0 is given by the expression (t) = cos(t + ) =cos(t) (=0) Step 1 of 2 : The expression for angular velocity as a function of time can be found by taking the derivative of (t) with respect to time. (t) = cos(t) d dt = - sin(t) and the expression for angular acceleration as a function of time is computed as follows; 2 d ( d )= d 2 = - cos(t) dt dt dt