Chapter 10

# Chapter 10 - 10 Rotation of a Rigid Object About a Fixed...

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10 CHAPTER OUTLINE 10.1 Angular Position, Velocity, and Acceleration 10.2 Rotational Kinematics: Rotational Motion with Constant Angular Acceleration 10.3 Angular and Linear Quantities 10.4 Rotational Energy 10.5 Calculation of Moments of Inertia 10.6 Torque Torque and Angular 10.7 Relationship Between Acceleration 10.8 Work, Power, and Energy in Rotational Motion Object 10.9 Rolling Motion of a Rigid Rotation of a Rigid Object About a Fixed Axis ANSWERS TO QUESTIONS Q10.1 1 rev/min, or π 30 rad/s. Into the wall (clockwise rotation). α = 0. FIG. Q10.1 Q10.2 + ± k , ± k Q10.3 Yes, they are valid provided that ω is measured in degrees per second and is measured in degrees per second-squared. Q10.4 The speedometer will be inaccurate. 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 . Q10.5 Smallest I is about x axis and largest I is about y axis. Q10.6 The moment of inertia would no longer be ML 2 12 if the mass was nonuniformly distributed, nor could it be calculated if the mass distribution was not known. Q10.7 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. Q10.8 No horizontal force acts on the pencil, so its center of mass moves straight down. Q10.9 You could measure the time that it takes the hanging object, m , to fall a measured distance after being released from rest. Using this information, the linear acceleration of the mass can be calculated, and then the torque on the rotating object and its angular acceleration. Q10.10 You could use ωα = t and va t = . The equation vR = is valid in this situation since aR = . Q10.11 The angular speed would decrease. The center of mass is farther from the pivot, but the moment of inertia increases also. 285

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286 Rotation of a Rigid Object About a Fixed Axis Q10.12 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 example 10.6 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. Q10.13 Compared to an axis through the center of mass, any other parallel axis will have larger average squared distance from the axis to the particles of which the object is composed.
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Chapter 10 - 10 Rotation of a Rigid Object About a Fixed...

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