12.43: Several forces act on a rigij r5f pw-t4b,bd body. If the resultant (net) force on the body is zero, which one of the following statements must 4ft,jwb5rp b -be true?

  97.39: A cylinder free to turnaro,sgakpcr 1fbk+ t;k4d5+nt3uund a fixed axis has a string wrapped around it as shown to 45 , +gu s3+;na pbcttkrf1kdkthe right. 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 rotam0zsh0xhg 87kte about an axis through its center. The stick starts from re z0sh8gmx0 7khst 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 9b5naf1nl+ pr when rotating with constant angular velocity. When the ana +rl5n 19fbpngular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without s6tqe)uj1 o4 hblipping 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 rotationalg2 5/hklpq:;5me rb z 2hk0wqr 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 id wwh.p.v:ny1 yeal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. Thpw.w y 1n:.yvhe 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 urib3 edgdc:,)niform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. g c3ir:d) ,deb 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 plan)fja 4,i rtzap 994v *xxzxh4pe. Which one of the following choices bestp,zfhx9r )t*azi94 j 4 vx4axp 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 left end. I2-yed ,tyxyq9csgf k9:n(nyg -ai*g 9t is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pivot wq*yc 2a9-(fgng9i-yt y n yexdkgs, 9:hen the rod is released?

  15.46: A uniform rod of mass M and length L is fixed to rotate about ajvo(ymj)s2t+ frictionless pivot located Lj myj)(t 2+vos/3 from one end. The rod is released from rest incrementally away from being perfectly vertical, 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 fixed to rotate cv4b:z blg7.c;uqyf0about 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 clockwise ;0b y4zgvc: ucq.fb7labout 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 ofp0a r0o1rmof, three long uniform cylinders with equal radii 01ramrp ,0oo fon the end 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,szox7(g mc bo/4l8; a bk:qa3g 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 g5yp-fr1 g iq i41.ayzz goo9/disks of equal mass each are mounted to rotate about an axis fixed through the r g.i4/o-f15p1yoqz azg 9yigcenter 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 and Y, have equal masses M but different3 *(j-qsis (jhxa f4yl radii such thq*sja 43 (ylf-(ihs jxat $r_x< r_y$. 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 au9o *t2 cwj6enw(9tnu j l*2jbnd radius R is pulled by a horizontal force F actij uc noetwu92(*2j 6bj9wl n*tng
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 clockwis5fq.pz8 zia9hut nm fk1uui;-kc 2 8g.fgh 6w3e about its ugazqc h n8h1 86 gfkz2-5;mi3u tif.pu9.fwkcenter 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 cm is / rx -u0cl:c9epgpd /g;f0uph4d l bk(connected about an axis through the center of the cylinder to a horizontal spring with spring constant 4.00 N/m. The cyx 0glh- bp 9u/ fr(eg p;dlck40pd:c/ulinder 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 equilibrium?

  01.39: Suppose the engine and propeller of a single engine plane are tubs; vaxnmfo 502v*g(a8iz w9urning in a clock wise direction with respect to tuwva2m ;o( 0bzgf8nxi v 5a*s9he pilot. The gyroscopic action of the moving parts will cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.