12.43: Several forces act on a rigid body. Igsroplh ss ; e9r8l mo25p-5g/f the resultant (net) force on the body is zero, which one of og9/l5r5;8h2o sp sp-gersm l the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string kyxk8 c+ 3xhzc22(qwo wrapped around it as shown to the right. The string is pulled with a force F equal to the cylinders weight. What is the acceleration of the xzw3 8kk 2y+2(hxocqcstring?

  16.16: A uniform stick is fixed to rotat* mdfwcm r6(* k-i(e(po alp0ve about an axis through its center. The stick starts from rest and rot*oi eap((v6c wk(*-mpr0lfmd ates 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 rot xe90zfk:+o vqating with constant angular velocity. When the angular velocity is reduced to one-third, the kie0o+9q xz:vkfnetic energy becomes

  12.33: A solid, uniform sphere rolls without slip :4p8 fe u1y;lzrzn: ruqi-eb5ping 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 rotatioj8p: (r8 /avo-nii+x zq .fsfbnal 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 ue cwt f)s4,xgf5g/ r4lniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined4 /g slf,rgtxcfe5)4w 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 have mass M an8tvzv g ph(497iek-ma o.00dnglm1 dn d radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of frim .zpneido1vgta-4 l8g0dh (km7 v9n 0ction 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 o j0: dx*rt*be5erk n;xn a rough inclined plane. Which one of the following choices best represents the type and direction of friction (if any) acting rr texbk* 0:jx;e* dn5on the cylinder as it rolls up the incline?

  14.43: A long rod of length L is pivoted about its left end. It ims7f4w2x9w ecj1 (rudz z 9u8vs released from an angle θabove the horizontal. What is the magnitude z fes v9zwuu7dwc xm(9r2j841of 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 fix+u 3+chhto+ e: l6ahcned to rotate about a frictionless pivot located L/3 from one end. The rod is released from rest incrementally away from being perfectl l ch++u:3thnha+6 ocey 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 about a f.36boffs.( me ns*)*vyxxql y m 2pud(rictionless 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 speedysf xenlso6( *b.fy mm)2v*3 .(xqpud of the center of mass about the pivot?

  06.24: A person tries to balance vertically each of three long unide.rp5mi 857fvbtgd gd7:6pj form cylinders with equal radii onm8v57 j5 p. btre6dd:7ifpg gd 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, have massenwx a+s1 r:iu;s $m_x$<$m_y$, 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 abrr balrdm 9iif*7:18 (akvt(m 7o/r cyout an axis fixed through the center of t 7r:v*87b irm(rmk lc(dat9a1yof /rihe 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 different radii sucwgg:z 73oyyx 8puhn5:h thggozy 3u:x:8phny w 57at $r_x< r_y$. 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 mas5gm,nrv8- nzvbe/( ;a-dedbq-4mmf :qw eya 7s M and radius R is pulled by a horizontal forc4d( yaeb m,/qfer-wq; n v7-5em8:ab-v gdnmze 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 6o3vq6lly q6 udisk of mass M and radius R rotates clockwise about its ceyqvul o3q6 6l6nter 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 cylindert+-s9twj :oht of mass M=2.00 kg and radius R=10.0 cm is connected about an axis through the center of the cylinder to at +9totw :jhs- 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 equilibrium?

  01.39: Suppose the engine and propeller of a s3us:a.eh/ z9t )za.7pqg p iu lt,id2cingle engine plane are turning in a clock wise dp9z.q2pzi uihctaeu 73 da/,t. g:)sl irection 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 sharp lefthand turn.