12.43: Several forces act on a rigid body. If the resultaxaovg9 hmvatfc0+3 r e;v6i mh8 e*+a0zm+6cxnt (net) force on the body is zero, which one of the following statements must be trueh*6vez03ac+t+80vvmc;gr+ao a xm9h6 x fem i?

  97.39: A cylinder free to turnaround a fixv0nw pr-n h80ued axis has a string wrapped around it as shown to the right. The string is pulled with a force F equal ton80phvrw-n 0u the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis through its center. imt*,ks) b9zy,kx6bpxzqj. hxz l 8)8The sk6 ,ljixmbxx)yz tsbh),z q9. *kz8 p8tick starts from rest 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 wsrj;yf*uun3wl 3n 20 q: 9hkmtith constant angular velocity. When thfu9t 0w:n3s; nmr *lj k2q3yuhe angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor along the ukh/gag cx*jiw6 3,h)jv xs: 8t6xip6$+x-axis$ (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, radius r, and rotational inertvx2j )4hed y :,wsh ( p7ftuu(phtsc/)ia $0.5mr^{2}$ . 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 ring each ha pnyy-fg4* ui;ve mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of friction for the disk and ring with the incline -gi n4*yyfu ;pare $μ_disk> μ_ring$.
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 vdjgoifv3)1 4solid disk and an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. Theo41ig3vdv )fj 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 ; 8mo5r35sp5yyxmbsp inclined plane. Which one of the following choices p 85y b3msxr sp5o5ym;best represents 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 my0z:j6 ,c+fn d3/ke;go v lovcw8sq7. It is released from an angle θabove the horizontal. What is the magnitude of t:7mycoqf ,/k;e0vlno63 +8 scwvj g zdhe angular acceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M and length L is fixed to rot 8-s-lhfb4d u:m5fk0dodj8spo - 7gk oate about a frictionless pivot located L/3 from one end. The rod is released from rest incrementally away from being perfectly vertical, resulting in the rod rotatingdu:h5--k 4sl7ogbs8fk oopj 8fd m0d- 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 massooas/edaj* ,(zjk d/3 M and length L is fixed to rotate about a frictionless pivot located L/3 from one end. Th/,*ao3 od j azd(ejs/ke stick is released from rest incrementally away from being perfectly vertical, resulting in the stick rotating 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 to balance verxdlj,iwvbl2 x3kc8vmd-*( 1i v; ii(r tically each of three long uniform cylinders with equal radii(bv, v-ivikwddri13 lj*xxmi(;c 8l 2 on the end of his 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, havenddvc9w2*r568ptvk i masses $m_x$<$m_y$, 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 mass+2l+pg+4r;pxzohcf c each are mounted to rotate about an axis fixed through thz+rcoc2x ++4 p gl;fhpe center of the disk. 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 but differu n6g,ha:- x /o: fe*msbo*:y6ei zrdeent radii such t:6xen e*/ de*b 6f:hosm,:yi-orgauzhat $r_x< r_y$. 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 /. -nepyzzral6 *lu8fis pulled by a horizontal force F 6n/rzelp *l8fa.-yuz acting
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+ktn)-vkp/6wf wc0/m2 m gx 1sowgq:n mass M and radius R rotates clockwise about its cen0wkg -fx1g nw qp2o6/) :/m+msvnkcw tter 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 conneu vewehp fu:sn8:(+;w cted 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. When released, tew:uf; shu+n(p8v we:he 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 propel:efqq;iy(+;sgvcl.k0;oa v4nr9 my np +c-uoler of a single engine plane are turning in a clock wise direction wikly +9qyrsaeno v; c;o(-u0v cm; . g+ifpqn4:th respect 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.