SM_chapter10

SM_chapter10 - 10 Rotation of a Rigid Object About a Fixed...

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10 Rotation of a Rigid Object About a Fixed Axis CHAPTER OUTLINE 10.1 Angular Position, Velocity, and Acceleration 10.2 Rotational Kinematics: Rotational Motion with Constant Angular Acceleration 10.3 Angular and Translational Quantities 10.4 Rotational Energy 10.5 Calculation of Moments of Inertia 10.6 Torque 10.7 Relationship Between Torque and Angular Acceleration 10.8 Work, Power, and Energy in Rotational Motion 10.9 Rolling Motion of a Rigid Object ANSWERS TO QUESTIONS Q10.1 1 rev / min, or π 30 rad / s. The direction is horizontally into the wall to represent clockwise rotation. The angular velocity is constant so α = 0. Q10.2 The vector angular velocity is in the direction + ˆ k . The vector angular acceleration has the direction ˆ k . *Q10.3 (i) answer (a). Smallest I is about x axis, along which the larger-mass balls lie. (ii) answer (c). The balls all lie at a distance from the z axis, which is perpendicular to both the x and y axes and passes through the origin. *Q10.4 (i) answer (d). The speedometer measures the number of revolutions per second of the tires. A larger tire will travel more distance in one full revolution as 2 r . (ii) answer (c). If the driver uses the gearshift and the gas pedal to keep the tachometer readings and the air speeds comparable before and after the tire switch, there should be no effect. *Q10.5 The accelerations are not equal, but greater in case (a). The string tension above the 5.1-kg object is less than its weight while the object is accelerating down. Q10.6 The object will start to rotate if the two forces act along different lines. Then the torques of the forces will not be equal in magnitude and opposite in direction. Q10.7 The angular speed ω would decrease. The center of mass is farther from the pivot, but the moment of inertia increases also. Q10.8 You could use ωα = t and v = at . The equation v = R is valid in this situation since aR = . 215 FIG. Q10.1
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Q10.9 The moment of inertia depends on the distribution of mass with respect to a given axis. If the axis is changed, then each bit of mass that makes up the object is a different distance from the axis. In an example in section 10.5 in the text, the moment of inertia of a uniform rigid rod about an axis perpendicular to the rod and passing through the center of mass is derived. If you spin a pencil back and forth about this axis, you will get a feeling for its stubbornness against changing rotation. Now change the axis about which you rotate it by spinning it back and forth about the axis that goes down the middle of the graphite. Easier, isn’t it? The moment of inertia about the graphite is much smaller, as the mass of the pencil is concentrated near this axis. Q10.10 A quick fl ip will set the hard–boiled egg spinning faster and more smoothly. Inside the raw egg, the yolk takes some time to start rotating. The raw egg also loses mechanical energy to internal uid friction.
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SM_chapter10 - 10 Rotation of a Rigid Object About a Fixed...

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