12.43: Several forces act on a rigid body. If the resultant (net) force on the i2 /fhs-ik or)body is z2sh-kir fo /)iero, which one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a ou ss*1z ln( k3*iipc6string wrapped around it as shown to the right. The string is pulled with a force F equal to the cylindl( s *13zu*oiink6s cpers weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis through its hvn73wanu( phlz /pcu4.xn/4 lsgf+- center. The stick starts fr4l7-lp/ wu/vp nus4nn3gh.hfzc x+(a om 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 /;qv mxiw.- f hdvtak)va00;g when rotating with constant angular velocity. When the angular velocity is reduced to one-third.af km;; vitgvhwx-d/0a0)v q, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipp4ib x4 h.d-+* mphu pm/cebso+ing 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 fy6o9qpxub 6to+t-o,5no +b8jul 8z xm, radius 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 uniformi vkf6oi;,j gg *vq-*c ring each have mass M and radius R. Each object begins purely rolling withoc* ;g gii- of*j6kv,vqut slipping down a rough inclined plane. The coefficients of friction 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 ideali u/; 9,cc9hv upkpvz* uniform ring each have 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 inclvipc/v*zp 9k,u 9u;c hine 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 witho ch9tyaq+ob- gx6r,2*lp3jx vp gz8 p,ut slipping on a rough inclined plane. Which one of the folqzla9y xcg p ,-o v2jh63p ,r8+gxbpt*lowing choices 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 lefvvb9me0 vj,8 jkcm*d273 2jef cpfuc3t end. It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pivot whejf 3*2 mb0 vk,9je8 jvpcufdm3cvc2 7en the rod is released?

  15.46: A uniform rod of ma p ymiv; hqz+p.n7fv98ss M and length L is fixed to rotate 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 rotating clockwise about tp;qv7i9.vp+ fm8 hnyzhe pivot. When the rod is horizontal, what is the magnitude of the tangential acceleration of its center of mass?

  16.50: A uniform stic6wn l.nsgr ju ke:l7v.wy6s:n4gb(4tk of mass M and length L is fixed to rotate about a frictionless pivot located L/3 from one end. The stick is released from rest incrementally away from being perfectly vertical, resulting in the stick rotating clgt:k l7( 6rybe6l4snwn vus:.n. jw 4gockwise 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 vertically each of three long uniform cyliux u1oixh 8ko mi1o:+,- j-ugbnders with equal radii on the end of his f81k,+gu o hu-1: -uiixmoojxbinger:
• 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( h7pd olb9-mo zltd74 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 each are mounted to rotate a/)lb0u vmm/lrt( *e euxu/ ttn2./ yihbout an axis fixed through the center of the disk. Each disk is initially at rest. Th/*/r m2vtyeuetul b/ht) .un /xlm i(0e 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 diaadx6w. f56 leii5gp 2sks, X and Y, have equal masses M but different radii such thldga.e 55xfiapi2 w6 6at $r_x< r_y$. 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 pulled by a1kqgeb:/*smy dyn;hzjpw kw2q d3g)1.8;qc a horizontal force F acting 1hk8w c2 qndy ;;qg.*/3p)jkmswe z1gqbda:y
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 M and radius R rot yir0yehb/0, v3q/e2fgezxf1 ates clockwise about its cent0vxyf3fh eeiyg1 ,//e0qbr z2 er 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 rad( nnx;fxi wvi)m(39y qius R=10.0 cm is connected 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. Wh)9i(; my n ivwxqf(nx3en 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 d1n/w:vt,t8yudcj 1 fengine plane are turning in a clock wise direction with respect to the pilot. The gyroscopic action ow d: 81ncyd,vj /f1ttuf the moving parts will cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.