12.43: Several forces act on a rigid body3ylv .a)s o1nu. If the resultant (net) force on the body is zero, which one of the following statements must be y )osa1u.ln3v true?

  97.39: A cylinder free to turnaround a b;lm-bu7- fml d(-ken-hd)ysde aj .-fixed axis has a string wrapped around it as shown n;l---)j bye7eb.s-md -(ka lhmddf uto the 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 stick is fixed to rotate a8f4*tw 6 :id+x*absdqng p:c bbout an axis through its center. The stick starts from rest and rotatewxnti d4 * 6::b+qpgcfab*d8ss 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 with cons,ye* 87v oreentant anguleveon*y ,8r7e ar velocity. When the angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping v)z,ma7 qifc:ns 4o*sl.pa7u pf,z0 hon 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,tst a69*eb qz* mvcj85 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 eanx v4zfb6r8q2chs 60ych have mass M and radius R. Each objezf x0n2q4ycbvh 8s 6r6ct begins purely rolling 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 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 massa1aoqp 8t+ dh4 M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. to1pd8 +q4 aha 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 cylinqhc61-6 jfv ohrcsx/-s 1pw 4*jyqt:g der rolls without slipping on a rough inclined plane. Which one of the following choicesj* p16 qtr:gsvqf1cwh s-y-o6/hxc4j 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 pivote e 0 ;+elu+ca0k7p3f5ewcew. rsmtlkl5pgy+ 7d about its left end. It is released from an angle ege+sl k 5cmlet+;wflp35w70r .py 7 k0cu+ea θabove 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 len636z6g8qmt swhb* gv kgth L is fixed to rotate about a frictionless pivot located L/3 from one end. The rod is released from rest increme36sk6w*z b8hgmv t6 gqntally 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.yokxovp;ij +x at7fae*7r 2fhmy/6 6 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 clockwif7*ixh ojpx.a 7f/ay;m6ev 2rk y+6 tose 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 each of three 8-venij ger8 g qn576 4jisnq(long uniform cylinders with equal radii on the end of his fg85j6sj8(-enq 7 nv4i iegrnqinger:
• 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 andgc)7lrdv(5 2is ffuq+Y, 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 mp ve3+k9i:ppn/dy7uzwp :v z9 ounted to rotate about an axis fixed through the center of the disk. Each disk is initiallykvp/:ppzy w3 9z+ie v: dn7pu9 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, Xs:+iezrja *1hi2 hyb1 and Y, have equal masses M but different radii such t:r zibi1* a1hyj2hse+hat $r_x< r_y$. 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 cylinde,b k+n4n00 lv p/c-+v*d rkn5 hzpduxdr with a mass M and radius R is pulled by a horizokdr*dl 0p -vzb c/p+ 0uv ,5hd+nknnx4ntal 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 dis5j)abhu w-1;kvuax;ql8y x f c:xe9;mk of mass M and radius R rotates clockwise about its center with an angular speed ;uk189l):-ahv uba;y qx fmc jx; 5xwe $ω_0$ . 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 connecq;z.psl2wf4it :h ee6 ted about an axis through the center of the cylinder ilh. fez2ewqps ;:46tto 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 of the cylinder when it returns to equilibrium?

  01.39: Suppose the engine and propeller of ; gwcyto 6y)ib k4rk9p.uh9b -a single engine plane are turning in a clock wise direction wiiur-9y)o 49t.b k hcw;py 6bgkth 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.