12.43: Several forces act on a g b5k. f:ed4r)o3wkforigid body. If the resultant (net) force on the body is zero, which one of the following statemeord f.kowe3gf: )5 bk4nts must be true?

  97.39: A cylinder free tr3ls0qoj62l(tbp:qj lb, ri, o turnaround a fixed axis has a string wrapped around it as shown to the right. The string is pulled with a force qt 6(l,j3p, r2ls r:ojiqbb0lF equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate abdmzi d-k 5yt6(xi0 ey2out an axis through its center. The stick starts from rest and rotates through an angle ofx i6zdki50y (2d-ymet $90^{\circ}$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 enh-)i7y:mw u osergy K when rotating with constant angular velocity. When the angular velocity is reduced to one-thirdhy7-s) o: wmiu, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slibr)* krpbrf8/ x2sl3 spping 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,1 +hs*)d.5nhkrogwkw 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 m+b4 yvcm8f d1*d rhx+have mass M and radius R. Each object begins purely rolling without slipping dowbmfvy hx+rdc+ *md148 n 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 mass p2+ ux nux1mh5:w-yis M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. 1yxsm-wu+x piu5 h2:n 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 dv dekuc4no6:iw +-jfux6f97 inclined plane. Which one of the following choices best represents the type and direction of friction (if any) acting on the cvdx4d6wu: f-uo 6kcn+ if7 je9ylinder as it rolls up the incline?

  14.43: A long rod of length L is pivoted about its left end. It is released fnqz)290 xd ztsqz3b f3rom an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pivot when the rot3qb0) fx2q9 zzn3z dsd is released?

  15.46: A uniform rod of mass M and length L is fixed t;i/,u z82/ol:rn cnhwjhkjr fngc.1(o 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 acceleration of its hj u wng ;rn2cohrnfj,l/i.:1 (8c /kzcenter of mass?

  16.50: A uniform stick of mlglcj )s n/)rwb u5.z9ass 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 thlul) w9 /z5g crn.)bjse tangential speed of the center of mass about the pivot?

  06.24: A person tries to balance vertically eachk;6ll g aq9*wb of three long uniform cylinders with equal radii on the end of 6qb ak9 lw*;lghis 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 a;sc:+om)p w.:q xf4wq it byb,ndY, 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 mounte:w))bp wy1b ek, v9u*z -sfpeybp*.axd to rotate about an axis fixed through the center of the disk. Each disk is initially at rest. The rauz -wyb9 vp bw1keyps) )ea,*b.px*:fdii 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, he-ydn-nlf (m kl321 ls+5ojwfh- ej5cave equal masses M but different radii such that5m-s(n w oj nlllf13 +eehc25-fjk-dy $r_x< r_y$. 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 wit0e7rm8xck p:)zxcr5th a mass M and radius R is pulled by a horizonm0px 7c 8)k5exc rtzr: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 and radius R rotates clockwise about qq,45z1nsvbj b.b 4rr96 znpwits center with an angular speedzb1v6n4. wn5qsr jqrbp9zb,4 $ω_0$ . 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 connec 09o 6(mwodwrt4s; uqnted 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 slipp0ron w6wuqtso ( m;49ding. 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 turning q.s /tvys(5dz a5tjy (in a clock wiyt at (q5/vd.ss5jz( yse direction with 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.