12.43: Several forces act on a rigidz(gcu5je3r4b zr 9/zey0u5v k body. If the resultant (net) force on the body is zero, which one uc40zrje5/5bgeuy 9z ( zk3rvof the following statements must be true?

  97.39: A cylinder free to turelcebq7e3 g41 ,pjlp4naround a fixed axis has a string wrapped around it as shown to the right. The string is pulled with a force pl,7 lqe14cbe4 3egj pF equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis*hsed 3 --*cb*yutb wf through its center. The stick starts fwh*ud y-bb3tec f* s*-rom 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 rotatingnfo 3a 0 /0veq9s8phb.ohb26h f7uznq with constant angul7 6 f.02b 93 sezanqphh0hqv uno8bfo/ar velocity. When the angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a flwx* u.-.hi:z lin ;v5c8w hmfloor 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, radj67ljm 8e-+avyposl 6ius 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 disk and an idh gq(.pfl1 kjj 5af,r pixgg(u.s 857xeal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a5f 7x ajl (5,fr pp8sx..qk1huj (ggig rough inclined 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 id 8 3/1hvgwtgnseal uniform ring each have mass M and radius R. Each object begins purely rwgv /s318 ntgholling without slipping down a rough inclined plane. 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 tew6z x4gc;8t rough inclined plane. Which one of the8 w;zxc6gte4 t following choices best 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. It is relejprrf+ g;40 hz8epu k6ased from an angle θabovep 48;hp +ukj0re zrfg6 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 f1j k rugl57qffp r0r0(rictionless pivot located L/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 cent5q07lrkf0f jr1ur( gp er of mass?

  16.50: A uniform stick of yk1lw zc29-azmass M and 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 rotating clockwise about its pivot. When the stick is horizontal, what is the tangential speed of the center of m19wkla-z cz y2ass about the pivot?

  06.24: A person tries to balance vertically each of three long uniform cylindek,un )qllz u4;de+on2rs with equal radii on the end of his finger:e,z o+ 2d;nl)un luq4k
• 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,Xhqd. m:h9q/ xyh+2 3qpfz)ghm 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 each are mounted tzdrs3:h9ma8pu rzx y+po(ms p.( /u5so rotate about an axis fixed thr:hpmm( (p3sssr .u5oxzz / +y 8udp9arough the center 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 bb/gj 5(-tiz (qyf8hx hut different radii such tha-/hh(5ifq ygbzt xj( 8t $r_x< r_y$. 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 massxnqv/5t4d .s o M and radius R is pulled by a horizon.ox dqvs4t5 n/tal force 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 xio9/9gje, y 2 ctysq2wliy6 2and radius R rotates clockwise about its ceny2,yw/c 9xj9egq si2y toi6l2 ter 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 cylinddlchggkk(1k 6eyt1zyu3,a5un+7 i a6 er of mass M=2.00 kg and 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 slippi1nkz eakt kh35 i1yg,y l(c6u6 ug7+adng. What is the speed of the center of the cylinder when it returns to equilibrium?

  01.39: Suppose the engine and propeller of a st: etcy n2asy,3:-ecixb(3xpingle engine plane are turning in a clock wise direction with respect to the pilot. 3:3sit,ycx( py na:e b-xect2The 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.