12.43: Several forces act on a rigid body. If the resultant (net) force on 9h td1cmy1gj -j45sghthe body is zero, which one 51y9shcmj 1 jt-g4dh gof the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wraee1xh y17k/.u 0lqkd8or.dp q pped around it as shown to the right. The string is pulled witq.h.oxyrd /k7keplqeu 1d1 08h a force F equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate i+7.m gg ndy9ibh. qm2*c0 gggabout an axis through its center. The stick starts from rest and rotate.n dg*imh gy i70gc+q2 g.mb9gs 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 conpsf*v ni* bxau6,u98s stant angular veu6b *v*9 sixp,fns a8ulocity. When the angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping/00 q/ w9rc j wfmuscua+-cv,e 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, :-6- jwwlgo n srg.v+jp*2zcc 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 uniform ring eac1q06 y;q hq tx 2ajv)ug(6zdyah have mass M and radius R. Each object begins purely rolling without slip(v hz2qqx1dq; agyt j 0ay)66uping 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 ideal uniform ring each havivy;b.mu88ag7-re dc jo+ m9b e mass M and radius R. Each object begins purely rolling with m8eb8rd 9jmc-oa .yv+7i;gubout slipping down a rough inclined 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 plane. Which7gjh6jxy 4zf( o0 hm1r one of the following choices best represents the type and direction of friction (if any) acting on thx1r m4zgh7fj(jyh 06oe cylinder as it rolls up the incline?

  14.43: A long rod of length L is pivoted about its left end. It is released fro lvj .j;r ji2b7s3sd-ym an angle θabove the horizs.irl;sd3 yj7j-vj b 2ontal. What is the magnitude of the angular acceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M and lengtbq-bl*kr vt )f h709:eol 1ieah 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 ro-*i9v )bka:e eo7rl1qftblh0d 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 i9dusx 3q f n)s(q1g.,ui:v b5kwmmf+ls fixed to rotate about a frictio3gl mw5q s,i(9xufv nmk:.dfq1b+ su)nless 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 tangential speed of the center of mass about the pivot?

  06.24: A person tries to balance vertic. lrqq,5mbi -ially each of three long uniform cylinders with equal radii on the end oflqr,q-i5i .b m 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 disksn)+ xd:.i. yu6hui lak,X andY, have 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 on6tfq3tw s:. 5ffz md+f equal mass each are mounted to rotate about an axis fixed through the center of the disk. Each disk is initially at rest. The radii of the disks f3f+m td.nf 5qts 6:zware $r_1 < r_2$. 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 different radirv b)c8;irjmrk7a9 uob3e3xom : */aei such tm);3a /vbkoem37c :jraexr o9b iur*8hat $r_x< r_y$. 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 rjnnppe8 +yqe x,;t99p v(sn f8adius R is pulled by a horizontal forp e8eq np,ysjp9nfvn+98xt; (ce 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 and radius R rotates clockwisecl0 pph /h3nq mgg5f1af3 45kj about its center with an angularagmc 1/3pkhfl4j0f5h5g n 3qp 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 radiu4keuq0(1b fm88nwf) z77c p: yswknpds 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, stretc)m8f( nf 1w0cpdw8yz4 sup7kk7: e qbnhing 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 returns to equilibrium?

  01.39: Suppose the engine and propeller of a single engine plak pg0r(zkvrh f(023p zi9-c ggne are turning in a clock wise direction with respect to the pilot. The gyroscopic action of the moving parts will cause the plane tokfv93(2-k rg0zrg(0p c zigp h move in which direction as the pilot tries to make a sharp lefthand turn.