12.43: Several forces act on a rigid brtv3j+ g ,o2zcody. If the resultant (net) force on the body is zero, which one of the following statements muzcvo g+r2j,3tst be true?

  97.39: A cylinder free to tni)qlq0xw-9 * gjy6vdurnaround a fixed axis has a string wrapped around it as shown to the right. The swi-q0l*jyn9 )6 qxgvdtring 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 c0a0 6fjj7biz bzkk6r0enter. The stick starts from rest and rotates through an 0 rkj6zfia06 70jbzkbangle 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 rotatinii2and4-tz16q 2 h 8t+y njsbig with constant angular velocity. When the angular velocity is reduced to one-third, the kinetic energy yt6qi nt n -h2z bad42i8s+ij1becomes

  12.33: A solid, uniform sphere rollskaqof 60 mq7 i ;xap7rl,9w+it without 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,nzr mz6w-: n.md zpz+2 radius 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 ideal uniform ring each hatw1efs xcvz,/35mqfh. ; 1y zh9b sne:ve mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of friction for the disk and rim 1 st59zf1 f;v:hb3xzyhc e .sqw/,neng 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 a sf c7*d1)vro 7vzn-ewn ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping downw1*vnd -7ec7z)v sfor 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 rough inclinav .v-p rro0x0ed plane. Which one of the following choices best represents the type and direction of friction (if any) acting on the cylinder as it rorpa.rv0 v-ox0lls up the incline?

  14.43: A long rod of length L is pivoted about its left end. It y *5/ea xtt:efis released from an angle θa xete*5/at:yf bove 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 frictio9 gj6vi),31hcvz flesnless 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 horie3fcz9vsh,1l j i)6gvzontal, 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 to8vo1:ejoxv/ m 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 horizo ex 1:o8mvvj/ontal, what is the tangential speed of the center of mass about the pivot?

  06.24: A person tries to balar 2js wn+;kk5i ix ad9cc c1(;99ftnypnce vertically each of three long uniform cylinders with equal radr9fa c(;ic;+c k95n px dn1jk2itw sy9ii 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 disks,X andY, hav-hci6 vfnrazlan8(w sih5x r9u012 s1e 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 moca-noqrn//vco0i1/ w unted to rotate about an axis fixed through the center of the disk. Each disk is initially at rest. The radii of nc1/va o-cr //wqni0o 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 differentz1i7tmuw5 dq; radii such that mduzw7i 15q;t $r_x< r_y$. 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 cy7yqi k5q6*brplinder with a mass M and radius R is pulled by a horizontal force F ack6qrp5y i bq*7ting
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 a/o -yqgd8m4w*0 u cu 4jcfea2qnd radius R rotates clockwise about its center with an aecdq482* jco0/ amwu-fgq u 4yngular 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 cokg. ny, p1m6cm 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 yc1p6g,mok. nfrom 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 turnih bwa ryc47ku z,im( i(w,e.0mng in a clock wise direction with resb(ki(,muh4 , w7mziarc0 e .ywpect 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.