12.43: Several forces act on a rigid body. If the resultant (net) force dq8z g( mi;oz2on the body is zeid (2z qo;mzg8ro, which one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixedl8fk kyfrf7nci-aw; ioejg0:k:s 74 / axis has a string wrapped around it as shown to the right. The strnki/fls8f fi-g kyrwje 47o 7:k0a:;cing is pulled with a force F equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis througcy+*ggmgy 3 ):llwb2bh its center. The stick starts from resb+ )lwbl2gcgyy:m* g 3t and rotates through an angle of $90^{\circ}$in a time of 1.0s. If the angular acceleration of the stick is constant, what is the angular speed of the stick about its rotation axis after one full revolution?

  98.22: A rotating fan blade has kinetic energy K when rotating with cqp8e 51m;fp*ls pq +joonstant angular; +j p*epp sqm51lfqo8 velocity. When the angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rbsj5k9tk9+qo -kibj6 olls without slipping on a floor along the $+x-axis$ (to the right). The rotational kinetic energy associated with the sphere about an axis of rotation through its center of mass along the $+z-axis$ (out of the plane of the page) is 20 Joules. What is the translational kinetic energy associated with the sphere?

  98.28: A solid disk has mass m, radiu ,s98crc-zy f5rxmwhz2ca+ +9b y)cnh s r, and rotational inertia $0.5mr^{2}$ . The disk is initially at rest. A constant force F acts tangential to the rim. What is the angular acceleration of the disk?

  13.39: An ideal uniform solid disk and an ideal uniform ri n4,xj*ru1 5clc wt;/yf:bdxlng each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of f:*bwjlfxn d5lctur/ y4;,1 cxriction for the disk and ring with the incline are $μ_disk> μ_ring$.
As each object rolls down the incline, which statement is correct about the force of friction from the incline on the objects?

  13.40:An ideal uniform solid disk and an ideal uniform ring each have mass M and+j;g nlhh10:usgb 72*d cqei7rzp3sf radius R. Each object begins purely rolling without slipping down a rough incline3fl0h nerczsp+ s i*g2d7j;g1hu:7b qd plane. The coefficients of friction for the disk and ring with the incline are $μ_disk> μ_ring$.
As the objects roll, what is the ratio of the ring’s angular acceleration to the disk’s angular acceleration calculated about an axis perpendicular to the object’s face and through its center of mass?

  17.31: A solid cylinder rolls without slipping on a rough inclined planz p)rv*:vr y0+tf+iw ae. Which one of the following choices best represents:z)rva+v0wi * ty +fpr the type and direction of friction (if any) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of length L is pivoted about its left end. Itincpn+95u 5a p:24 ttbijdiq) is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of theciqiiujb +5 9np2)p:tn td5 4a rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M and length L is fixed to rotate abs6/d vc+70vz*th h6tja txy:r out a frictionless pivot located L/3 from one end. The rod is released from rest incrementally away from being h 6xttzrv6yhj0 svd*ca7+: /tperfectly vertical, resulting in the rod rotating clockwise about the pivot. When the rod is horizontal, what is the magnitude of the tangential acceleration of its center of mass?

  16.50: A uniform stick of mass M and length L is fixed to rotate about a frict :-pnzg5x 6nrqionless pivot located L/3 from one end. The stick is released from rest incrementally away from being perfectly vertical, resulting in the stick rotatinnqgn5z 6pxr:- g clockwise about its pivot. When the stick is horizontal, what is the tangential speed of the center of mass about the pivot?

  06.24: A person tries tg;h lmn1a.y9d3* qxwukz)l:qo balance vertically each of three long uniform cylinders with equal radii on the end of his :* lqkw;1h l yxdqa93u.mzgn)finger:
• A wood cylinder of mass m and length L with moment of inertia I
• A bamboo cylinder of mass m and length 3L with moment of inertia 9I
• A concrete cylinder of mass 4m and length 2L with moment of inertia 16I Which object is the easiest to balance and why?

  14.39: Two uniform disks,X andY, have mass9b yl,c6j9gq 9 xwqt6zes $m_x$<$m_y$, equal radii, and equal initial non- zero kinetic energies. Each disk rotates counterclockwise in the plane of the page about a fixed frictionless axis through its center. As shown in the figure, a force F is applied tangent to each disk at its right edge for the same amount of time. After the forces are applied, let L represent the magnitude of the angular momentum about the center of a disk and K represent the kinetic energy of a disk. Which one of the following choices correctly compares these quantities for disk X anddisk Y?

  04.46: Two solid uniform disks of equal masi6/zu49vhkx 3s7r v fms each are mounted to rotate about an axis fixed through the center of the di6vmxv39 hu r74kf i/zssk. Each disk is initially at rest. The radii of the disks are $r_1 < r_2$. A force F is applied to each disk at its edge for the same amount of time. Assume that friction is negligible. What statement is true about the kinetic energy K and magnitude of angular momentum L of the disks?

  15.35: Two uniform disks, X and Y, have equal masses M smzhjw. 15qt8oh)rr0 but different radii such t1.rh8q)mh50wj z sr othat $r_x< r_y$. Both disks initially are at rest. A force F is applied tangent to each disk at its right edge for the same amount of time. As a result, each disk rotates counterclockwise in the plane of the page about a fixed frictionless axis through its center. Which one of the following choices correctly compares the magnitudes of angular momentum L about the center axis and total kinetic energy K of disk X and disk Y?

  10.40: A uniform, solid cylinder with a mass M and radius R is p7a 0k.l9tgbk o6 fckp6ulled by a horizontal force F actinlkcbt 760 kkp foag.69g
through the center as shown. The cylinder rolls to the right without slipping. What is the magnitude of the force of friction between the cylinder and the ground?

  14.49: A solid, uniform disk of mass Mx h)fb)pm;w;f and radius R rotates clockwise about its c)hfxwbpm f); ;enter with an angular speed $ω_0$ . The disk then is placed onto a horizontal surface and begins moving only to the right, slipping as it rolls. The coefficient of friction between the floor and the disk is μ and the
frictional force is considered constant throughout the motion. What is the angular speed of the disk when the disk starts rolling without slipping?

  09.40: A uniform solid cylinder of mass M=2.00 kg and radius R=10.0 cm is conns 0w;0pocw, ljzgm o69ected about an axis through the center of the cylinder to a horizontal spring with spring constant 4.00 N/m. The cylinder is pulled back, stretching the spring 1.00 m from equilibrium. Whej0zwwmplc s;g o ,069on released, the cylinder rolls without slipping. What is the speed of the center of the cylinder when it returns to equilibrium?

  01.39: Suppose the engine and propeller of a single engine plane are t. lds;-f fq*jwurning in a clock wise direction with respej f* .q;w-ldfsct to the pilot. The gyroscopic action of the moving parts will cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.