12.43: Several forces act on a rigid body. If the resultant (net) force on the z gu5fcifc73( ns,sld5 ccje)( f4)llbody is zero, which one of the following statements 7zcj cfs)n53lfgc5c(d,u4f e(ll)si must be true?

  97.39: A cylinder free to turnarounv x 9tpsh0+m33*d quuz5jazu3 d a fixed axis has a string wrapped around it as shown to the ri9m3h53ua*su+j t xpvq zu30d zght. The 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 through its cent:e/yvt x/ 5d8x9nqyek j ci*,yer. The sticktyjye*kq8c yiv/x /e,x:9n5d 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 wueodbe,i0fjr 8m s ,6+hen rotating with constant angular velocity. When the angular velocii + 860edmb,e sjf,ourty is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slippg 2ch 0g7rk;jning 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 rot jqoyz6c+6.g-7 op pgeational 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 each have mass Mb. i8gg9knrpf 85gylt+ 3s;qw and radius R. Each object begins purely rolling without slipping down a rough inclinnb+wl8 fr g9 y8its;g k.qg5p3ed 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 (a)na5 e8:;q+khej sv+r j: crrzi1zgdisk 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 eeq:g;ar()j 1 zv8 ksn+zjirrch+:a5 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 cylinderkrf8x:vf 1 h2d,ihs- :kj5tba rolls without slipping on a rough inclined plane. Which one of the following choices best represents the type and direc8:kjak5vifdh tsrhbx:f -2 ,1tion of friction (if any) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of length L is 9co9xcaz4+ 6o-g ptqnpivoted about its left end. It is released from an angle θabove the horizontal. What is ga-no96oc ct+p xq z49the magnitude of the angular acceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod of mlcw4 o3zh8c 3gf ain:lov.( )qass 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 veqwo)all3c .o h 4i8zgf(v3cn:rtical, resulting in the rod 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 is fixe4lwv1us 9hg y1be.jef1jm:8hd to rotate about a frictionless pivot located L/3 from one w41.v8e:g hjj91l1byme shfuend. 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 vertically each of three long uniform cylsgjly.9p.:munv hl7g.zi 6g 7inders with equal radii on the en: 7ul79s..hzy gmg lnpi.jg6v d 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, haw3xx m:q+ f7x+xqna,o ve 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 mo5ayhjc w9v 3von*xj0 1unted to rotate about an axis fixed through the center of the d5 a 3*v0vhjjno wxy19cisk. 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 differend*ew twd(:j 5fx ,o,dem 0)vnocp h8g0t radii such t, 5dfd dp ghjxwvo w,*) (0emncoe:08that $r_x< r_y$. 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 radiu a9. avyc/ 67ouqts+ klaxz6y*s R is pulled by a horizontal force F acting 96syvcaxz+6/laq uoyta*.k 7
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 awwkr,o t+5s5z nd radius R rotates clockwise about its cente+5sww tr5o, kzr 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 c 9 sdyi4ypc8+3yg;myb m 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 returns to equilibri 3ci;dy s84mbpy+gy y9um?

  01.39: Suppose the engine and propel p3twv8 npnrgzuo6099ler of a single engine plane are turning in a clock wise direction with respect to the pilot. The gyroscopic action of the moving parts will cause the plane6gnz p ur39v wnot98p0 to move in which direction as the pilot tries to make a sharp lefthand turn.