12.43: Several forces act on a rigid body. If 6p2g2 hi u,e*;jk+ gmave. qt3gw5zd pthe resultant (net) force on the body im*326tpkewh.2dj;z +ei vg gapq,5u gs zero, which one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axi:x y,cf*z9s9w mf,3swsn3oo f s has a string wrapped around it as shown to the right. The string is pulled with a force F equal to the cylinders weight. What is the acceler,swc: 9sf3o* nsoxy 9,ff wz3mation of the string?

  16.16: A uniform stick is fixed to rotate about an axis through its cem)rvc 65vyqyemm.w7 )nter. The stick starts from rest 5y6rm.c)wmm e7y v)qv 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 u4dp54xpzkt dti- 5e)1 9)vsr k:oavgwhen rotating with constant angular velocity. When the angular velocity is reduced to one-third, the kinetic energi 1)4:9kavkvg)s tztppd5 o4d5 eu-rxy becomes

  12.33: A solid, uniform sphere rolls without sl p,o zrm(ej0k3ipping 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 ma fyez *10lcjfa8 2dw7oss m, 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 d+xz; br6yk hc ei+j57fisk and an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of frictionhe+by j c7 6ikrf;5xz+ 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 di *)nku:kji 6vesk and an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients k 6 e)v:ku*jinof 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 :bimb;5b6j w a*w:p e bse:ky2on a rough inclined plane. Which one of the following choices best represents the type and direction of friction (if any) acting on the cy;w:p2ky:biew jb 5bb*:ea6 smlinder as it rolls up the incline?

  14.43: A long rod of ldeeq r985yn x;ength L is pivoted about its left end. It is released from an angle θabov edry5;x9ne 8qe the horizontal. 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 length L is fixed to rotate about a frictionlq qc4kc qk:* ua2j9o tih(m9b6ess pivot located L/3 from one end. The rod is released from rest incrementally away from being perfectly vertical, resulting in the rod rot6tqmk:9uob94* (cikqqhaj c2ating 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 an8 3sa g,a4tqx.icsg)nkl *5jmtp .n*xd 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 rotatingqx53 4ak*ggtmpanxsntj ,cis)*8.. l 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 xt8 nmmt,69kn5e (jpmvertically each of three long uniform cylinders with equal radii on the emntj pt5 6xmk,8m (9nend 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, have massesjeqdis: .+-o klrh-wqi.4ir c /7(ddl $m_x$<$m_y$, 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 about rn,n 4s s)d (vt9e5lolr88vbt an axis fixed through the center of the disk. Each disk is initially at rest. The radii of the dil vs()nrln8tbvdo89 r4s5,e t sks 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, heo p++s8jl,k 7z;tp *np.nh gzave equal masses M but different radii such te+*lg8; +pjn p.ktso7 ,hzzn phat $r_x< r_y$. 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 cylin: g72-lyb)9x. xje:+xrgg8teuutq fh der with a mass M and radius R is pulled by a horizontal force F actinggtyeu:7xg+9erx jg t q)u.l8 f:h2 bx-
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 radiu4k7d-y cz*ceg s R rotates clockwise about its center with an anguldce4 zg*y-7ck ar 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 ans7 zd+x,bco;iq lupd)ej1kt m1 48,fgd 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 thzxu14t b);pm1df,8jogl+ sqed k ci7,e center of the cylinder when it returns to equilibrium?

  01.39: Suppose the engine and propeller of a single engine plane are tk /9i0h fjtcb*urning in a clock wise direction with 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 sjhc9if/0 b kt*harp lefthand turn.