12.43: Several forces act q dov,bb).p(v:s:uuu on a rigid body. If the resultant (net) force on the body is zero, which one of the following statements muuu).ob bduv,:(sqp v:st be true?

  97.39: A cylinder free to turnaround a fixed axis h7b f e.xes ih 8py30eo;,2qzpu4sg7wgas a string wrapped around it as shown to the;s2ui s8e7e3 pbzq7f e ogx4wg0 p.yh, 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 stin1fp mg /;(k-g)j(f)yeshk6pvks x u4ck is fixed to rotate about an axis through its center. The stick starf1vg4)skp;)fjgmxpk - e6/s uyk( (hnts 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 when rotating bod)pffkc r,tajd7 5 no7/-hetd022gwith constant angfj,t5 tdr2n7o2p) a- 0 gh7k/db cfdeoular velocity. When the angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls wip:zqh 8q;9whh u ;y6nbthout slipping 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 rotational inertiglm-n0xb bk wv)/ 3ul4a $0.5mr^{2}$ . 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 unifor0.o kq. yrp zr.-v4lrjm ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of oj. z.rp-.kqrryvl04 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 so k30e-h1zdql m -p/;s1e.j bmgait9ukun4be-lid disk 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 friction for th.k -u9jmiudgh1 qzkbb;s0etnale/43pe1-m - e 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 cylin1g j tkx 7:69grmyasitpkm4**der rolls without slipping on a rough inclined plane. Which one of the following choices best represents the type and direction of friction (if any) acting on the ci71 9pymgk4 t:6srmkg t**ax jylinder as it rolls up the incline?

  14.43: A long rod of length L is pivotednzw*u 3 r98g)krd )ndd about its left end. It is released from an angle θabove the horizontal. What is the magnitude of the3 k * r)g8)ddnrzdn9uw angular acceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M and length L / ytqb-q4v l1 -2p( pdi+osda3qg9x kwis fixed to rotate about a frictionless pivot located L/34/vlbyid 9g x o23w pp dk(asq+1qtq-- 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 ro-(6gbzg72irq 0euvgx tate about a frictionless pivot located L/3 from one end. The stick is released from rest incrementally away from being perfectly vertical, resulting 6g7gx-r i qbu(z0egv 2in 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 eac r yw:rs teg-m420nurj9h8pw5h of three long uniform cylinders with 8j -g 2shwn yermp9r4: 5twur0equal radii on 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 diz.38kjf v ww0ksks,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 of equal mass w6wny jni3dk 62 yw 0mcng7r;3each are mounted to rotate about an axis fixed through the center of the disk. Each disk is initially at rest. The radii3 n3wwnnw mg7c ikdyjy6 r;620 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 equl/j2 hkhde)*9i ihs yygt(v79al masses M but different radii such thh(2)y*ti h ky/jh 7glsived99at $r_x< r_y$. 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 rd q-y q7y 9:f3qrfy3ybadius R is pulled by a horizontal force7by 93dqqyf: qr 3yfy- 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 clockwise abouf;wy20( q qtjpt its centfq0w jq2; (ypter 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 i. tjj5n3a 8pmof mass M=2.00 kg and radius R=10.0 cm is connected about an axis through the center of the cylinder to a pnji85mt.j3a 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 propelsv chs-x ei 9fn.(+pf3.e/lu oler 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 plane to move in which direction au s.exfh9sf 3+ vi./l -(nepocs the pilot tries to make a sharp lefthand turn.