12.43: Several forces act on a rigid body. If the resultant (net) foyzk g;ikm j7;zm b+c4 ny18l4yrce on the body is zero, which one of the following statemen4g lmzbj;iyn y;+87 kz1ykc4mts must be true?

  97.39: A cylinder free t0 mhfe :cn.;iyo turnaround a fixed axis has a string wrapped around it as shown to the right. The string is pulled wn i hycf.;:0emith a force F equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is ;oo*8da wu/ ).vyofv wfixed to rotate about an axis through its center. The stick starts from rest and wd.wyvo av*o8u/of ; )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 fanazhc 4gc2./p z,o s/mrxxrfmj 3,xx:) blade has kinetic energy K when rotating with constant angular velocity. When the angular velocity is reduced to one-third, the kin .zrgz,hxx cro3,s/x:jxm4cm2 /fa)petic energy becomes

  12.33: A solid, uniform sphere rolls withou p m6l.)bza3n-ev 0lv;qje3 cwt 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,y si2e/ cg8yh0psl:e4 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 h+dhk7xx3fwtr2h0 oo *ave mass M and radius R. Each object begins purely rolling without slippinh0o w3fx72 kt*xo+h rdg down a 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 ideal ufpo5,eac n/yx j8p 0a:niform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough incl5f0ep,:xy8 cpa/ onj ained 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 wityv fp8 5 r1-zyntlx3)thout slipping on a rough inclined plane. Which one of the following choices best represents the type and direction of friction (if any) acting on thr lt8z 15vypxf-)ty3ne cylinder as it rolls up the incline?

  14.43: A long rod of length L is pivoted about ir7o8z1) ;otdhqd3 0,6i8 ttkfzkvwg yts left end. It is released from an angle θabove the horizontal. What is the magnitude of the angular accelera)itt8ov8y36z,k oqr f0;7 1gzddwthktion of the rod about the pivot when the rod is released?

  15.46: A uniform rod of man5k 5)9m ubeptss M and length L is fixed to rotate about a frictionless pivot located L/3 from one end. The rod is released fro)tk59up mebn5m 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 Ml e3iun+sp u*8 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 3p8ine lu* su+center of mass about the pivot?

  06.24: A person tries to balance vertically each of three long unif bj xa zi5a. )drt,w7;ygyd:(aorm cylinders with equal radii on the end of his finger: 7t)gdra a i;:wby dy(5a,j .xz
• 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 disb41a:;y:w 7-rlyk sbsq rcbi;+ cm j2aks,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 each are mounted to rotate :n*mir-8u ddgabout an axis fixed through the center of the disk. Each disk is initially at rest. The ra mingru *d:d-8dii 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 differe//i:h1ek0wn mqaf zq 8nt radii such that :1 eq//08f nzmkhaiqw $r_x< r_y$. 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 and3zs4v *fgtttb-u9xvu* -3k yh radius R is pulled by a horizontal force 3t9vy * b-tvzf-kt*s ug4h3ux 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 about i 5x9z4x 6xgubcts center u9cbg5x6 4xzxwith 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 conu ; web+9;vgygnected 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 slipping. What is the speed of the center wu+ev9gyb; g; of the cylinder when it returns to equilibrium?

  01.39: Suppose the engine and propeller of a single engine plvv ns.lsk,hr;20a v- aane 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 whnlrvk-sa.2 h ,0vv s;aich direction as the pilot tries to make a sharp lefthand turn.