12.43: Several forces act on a rigid body. If the res0 xcdt 3m8d0khultant (net) force on the bod0x8hmdc 30k tdy is zero, which one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis h22y5xdjq w wg4jyx9:oas a string wrapped around it as shown to the right. jq:5x2y9 owd42wjxgyThe string 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 thro/nrjx 1 )5vkn)c5ovuuugh its center. The u5k1xuc5) /nno) vvrjstick 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 with conswqb-ojrc(33z,*j2 xt bl ak-etant angular velocity. When the angular veloc2 3tq* kjxoe(z,a-rw- jc bbl3ity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slippik 0-dvt,.ezr 7 0nss.qaui; gl. xyg*ong 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, radius r, and rotational inbcno4j-d99 c,d;)j z(v ufxqr ertia $0.5mr^{2}$ . 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 (m7rfx ypt/(lws:5 avuniform 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 rin7( s:wpxyf /rm(a5tvl g 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 masmn z+1 1od0e,ltveirw:ng f4:s M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficf1etder :m+1:vi4,l wo0 nng zients 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 wim(u u.ydj.rr*kl s.8dthout slipping on a rough inclined plane. Which one of the following choices best represents the type and dird. *ym.s(r8urku l.dj ection of friction (if any) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of lpdq9/h(xv8 :z 0 oh-rye94vrmwx l m:mength L is pivoted about its left end. It is released from an angle θabove the horizontal. What is the magnitude of ther:qdphovwm9vzl (/hxm 9 xy:084rme - 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 fix7ou02k t mqylw2bg71u ed 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 0l2bymu71uow t7q 2kg 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 fricti+ vf)9pior:vdwb8y/zonless pivot located L/3 from one end. The 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 tangentiaf8 )9irodvw: p+/zybv l speed of the center of mass about the pivot?

  06.24: A person tries to 8vrxfz x)gby n*o, f6tc sm+-51hwpj/balance vertically each of three long uniform cylinders with equal radii on the end of his finger: , wyxzc+p fr-51 hx/bg8t6*jsno) mf v
• 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 mare8o*zh 3 +c4 f6 ;cltyz9c* pmaaiwf:sses $m_x$<$m_y$, 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 t4r:ede2x,1 (nu ,i2yclk)s+eoov vmzo rotate about an axis fixed throecur, :mvoe) 1 nlo+y4d2x,k( vz2ei sugh the 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 an1 dl7rh y.j xe49ikcz.d Y, have equal masses M but different radii such th.lie.jdhz 1y97c x4k rat $r_x< r_y$. 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 mafcz8xtn 1kh;1 ss M and radius R is pulled by a horizontal force; 1z1hf n8tkxc F 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 mass M+*(t ck zez8j.yg5zal and radius R rotates clockwise about its center wi e5k( y.zz+t*zaglc8jth 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 soli1jjfu2j.- khmj9s z w kmw 3/8p7rqr+pd cylinder of mass M=2.00 kg and radius 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. When released, the cylinder rolls without slipping. What is the speed of the center of the cylinder when it returz kpkrj8w1 +jh-/p2 m9f7qmwjj u 3.srns to equilibrium?

  01.39: Suppose the engine and propeller of a single engine plane are fa* rl 3bba(v,272z5cuix spvturning in a clock wise direction with respect to the pilot. The gyroscor2u(fic3,7va p2l* azv bxb5spic action of the moving parts will cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.