12.43: Several forces act on a rigid body. If the resultai 7 qnl-h7ueecoxb4w9e 19wd9nt (net) force on the body is zero, which one of the following statements must be true?1eq lxw9u9c-n 4owd9e7ihe7b

  97.39: A cylinder free 0fku) q*dlh) tto turnaround a fixed axis has a string wrapped around it as shown to the right. The string is pulled with a force F equal to the cylinders weight. What is the accetd) q)*k0fhluleration of the string?

  16.16: A uniform stick is fixed tkv1bbexna:-4qg tq9gmj t: 0*o rotate about an axis through its center. The stick starts from res9vtmketq:njb 14:a0x*q -gbgt 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 energk mnhr00 pes09t:ogl; y K when rotating with constant angular velocity. When the angular velocity is reduceetksrl o09gn:0p0 ; hmd to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor along t(m-3ammc6 5emk1t xhywhb2 9ihe $+x-axis$ (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 in+ 6b gkiomf7b30jj.eqertia $0.5mr^{2}$ . 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 have mass M .n54-ysizj o.qgr vngc+ 0au.and radius R. uz.5g4rqj0nas ov.+.-gnyc i Each object 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 wop td06jgub),zf(n33pm2s o 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 frict0su6gob)pt oj 23np(3 zmfdw ,ion 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 6+)fxtusedh 6 rough inclined plane. Which one of the following choices best represents the type and direction of friction (if any) acti sefu+hx dt66)ng on the cylinder as it rolls up the incline?

  14.43: A long rod of length L is pivoted about its left enlm76do0zx -n xd. It is released from an angle θabove the horizontal. Whd0lzomx6x -7n at 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 ucp ;9fng;e)nM and length L is fixed to rotate about a frictionless 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 accelecen n f;pgu);9ration of its center of mass?

  16.50: A uniform stick of mass M and length L is fixed to rotate about a fricb:k -bylxw:k0ruf/x) tionless pivot located L/3 from one end. The stick is released from rest increx:kfrb/- ) k0 luxw:ybmentally 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 mass about the pivot?

  06.24: A person tries to balance vertically each of threebm*jy9nc k0, g long uniform cylinders with equal radii on the end*ym ngk90, bjc 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, havot) 0 reivqy6l6 *axm5e 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 disku:oj* du g/5ods of equal mass each are mounted to rotate about an axis fixed through the center of 5 ojuodd /:u*gthe 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 cq dnvh3mz (cmkzb3hvf86 6svb0b 87;, have equal masses M but different radii such th h8;vv( 6bmvz6sn 3fzm08hdcckb q73bat $r_x< r_y$. 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 e x e51gi-vxf1mass M and radius R is pulled by a horizonta1f1v 5igeex-xl 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 and ras/ccznb zobvc ;n0 u250:rh: kdius R rotates clockwise about its center withzcu :nv/ bs0hrbz 5c:k0c2;no 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 p 5hbyu6wu0e / 3gz-x ht6.wyxradius R=10.0 cm is connected about an axis through the center of the cylinder to a horizontal spring w-6by x/5g6e.uwyw3 x0huph t zith 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 )ygbm(rhz5 , mpropeller 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 plrzy)mg5 ,b(m hane to move in which direction as the pilot tries to make a sharp lefthand turn.