phsx205_hw08b_solutions

phsx205_hw08b_solutions - Phys 205 Chapter 8 Solutions(Part...

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Phys 205 Chapter 8 Solutions (Part 2) 8.44 Which has a larger moment of inertia, a disc of mass 20 kg or a hoop of mass 15 kg with the same radius? This is a moment of inertia problem. Given: Masses: m d = 20 kg , m h = 15 kg Radii: r d = r h = R We want to find which of these objects has a larger moment of inertia. I’ll set this up as a ratio. I disc I hoop = 1 2 m d R 2 m h R 2 = m d 2 m h = 20 kg 2(15 kg) = 0 . 67 The less massive hoop still has the larger moment of inertia. 8.46 If the mass of a wheel is increased by a factor of 2 and the radius is increased by a factor of 1.5, by what factor is the moment of inertia increased? Model the wheel as a solid disc. This is a moment of inertia problem. Given: Masses: m 0 = 2 m Radii: R 0 = 1 . 5 R We want to find the factor by which the moment of inertia has increased. Again, this is easy to do with a ratio. I 0 disc I disc = 1 2 m 0 R 0 2 1 2 mR 2 = (2 m )(1 . 5 R ) 2 mR 2 = 4 . 5 8.49 The moment of inertia for a square plate of mass M and length L that rotates about an axis perpendicular to the plane of the plate and passing through its center is ML 2 / 6 (see figure). What is the moment of inertia of the same plate when it is rotated about an axis that lies along one edge of the plate (see figure)? Fig. P8-49, p. 276 This is a moment of inertia problem. Given the moment of inertia of an object in one configuration, we want to find the moment of inertia in a different configuration. In the new configuration, more of the mass is farther from the axis of rotation compared to the initial configuration. Thus, we should expect the moment of inertia to increase. If we examine Table 8.2, the second configuration is similar to the rod pivoted at one end (the lower left on the table). If we stretch out the rod vertically, we are not changing the distance of any piece of mass from the axis of rotation and thus, we should expect the moment of inertia to be the same.
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