Chapter 11

# Chapter 11 - 11 Angular Momentum CHAPTER OUTLINE 11.1 11.2...

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11 CHAPTER OUTLINE 11.1 The Vector Product and Torque 11.2 Angular Momentum 11.3 Angular Momentum of a Rotating Rigid Object 11.4 Conservation of Angular Momentum 11.5 The Motion of Gyroscopes and Tops 11.6 Angular Momentum as a Fundamental Quantity Angular Momentum ANSWERS TO QUESTIONS Q11.1 No to both questions. An axis of rotation must be defined to calculate the torque acting on an object. The moment arm of each force is measured from the axis. Q11.2 A B C ⋅× af is a scalar quantity, since BC × is a vector. Since AB is a scalar, and the cross product between a scalar and a vector is not defined, AB C is undefined. Q11.3 (a) Down–cross–left is away from you: −×− =− ±± ± jik ej (b) Left–cross–down is toward you: −×− = ± ij k FIG. Q11.3 Q11.4 The torque about the point of application of the force is zero. Q11.5 You cannot conclude anything about the magnitude of the angular momentum vector without first defining your axis of rotation. Its direction will be perpendicular to its velocity, but you cannot tell its direction in three-dimensional space until an axis is specified. Q11.6 Yes. If the particles are moving in a straight line, then the angular momentum of the particles about any point on the path is zero. Q11.7 Its angular momentum about that axis is constant in time. You cannot conclude anything about the magnitude of the angular momentum. Q11.8 No. The angular momentum about any axis that does not lie along the instantaneous line of motion of the ball is nonzero. 325

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326 Angular Momentum Q11.9 There must be two rotors to balance the torques on the body of the helicopter. If it had only one rotor, the engine would cause the body of the helicopter to swing around rapidly with angular momentum opposite to the rotor. Q11.10 The angular momentum of the particle about the center of rotation is constant. The angular momentum about any point that does not lie along the axis through the center of rotation and perpendicular to the plane of motion of the particle is not constant in time. Q11.11 The long pole has a large moment of inertia about an axis along the rope. An unbalanced torque will then produce only a small angular acceleration of the performer-pole system, to extend the time available for getting back in balance. To keep the center of mass above the rope, the performer can shift the pole left or right, instead of having to bend his body around. The pole sags down at the ends to lower the system center of gravity. Q11.12 The diver leaves the platform with some angular momentum about a horizontal axis through her center of mass. When she draws up her legs, her moment of inertia decreases and her angular speed increases for conservation of angular momentum. Straightening out again slows her rotation. Q11.13 Suppose we look at the motorcycle moving to the right. Its drive wheel is turning clockwise. The wheel speeds up when it leaves the ground. No outside torque about its center of mass acts on the airborne cycle, so its angular momentum is conserved. As the drive wheel’s clockwise angular momentum increases, the frame of the cycle acquires counterclockwise angular momentum. The
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## This homework help was uploaded on 04/13/2008 for the course PHYS 211 taught by Professor Shannon during the Spring '08 term at MSU Bozeman.

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Chapter 11 - 11 Angular Momentum CHAPTER OUTLINE 11.1 11.2...

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