12.43: Several forces act on a rigid body. Ifssd .u.iupyu .5pcg,2 the resultant (net) force on the body is zero, which one of the followingup.,cuu. 2 p.iy 5sgds statements must be true?

  97.39: A cylinder free to turnaround a fixed axis hasbbx.tyrem3 0xq;7 c*m a string wrapped around it as shown to the right. The string is pulled with a force F equal to the cylinders weight.mxyr x0. 3q;ct*7bb em What is the acceleration of the string?

  16.16: A uniform stick5ub6bosk 58,gqk3 hxd is fixed to rotate about an axis through its center. The stick starts from rest and ro3bd6k 8o5kxqsh g5b, utates 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 w 9w .bqtva22dfith constant angular velocity. When the angular velocity is reduced to one-third, the kinetic energy becomes9 w2tafb q2vd.

  12.33: A solid, uniform spf bd2h7,k0gw* i/fcflhere rolls 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, radius r, and rotational cqxto dm:*y (uw *m2+,bgg25 .frqtguinertia $0.5mr^{2}$ . 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 p1)8 6rg uxxvjring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclin up 6xx1vg)8jred 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 e o,ux1 y7 su,0pne;c. hfprl3aach have mass M and radius R. Each object begins purely rolling with 3h euyc,a7uxop;r.fsl10p n,out slipping down 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 incline7vkyhh-(k x*s ,1oe o7+o,qnkrpn 5tm hm1jt5d plane. Which one of th 1o v5+tn7 hprnsh-5mqkok1t 7m,,(x k*jyoehe following choices 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 li)pf83sm0 lnmmkn j1 8jy5u4vength L is pivoted about its left end. It is released from an angle θabove the horizontal.8mvfn)mk j8 34i1n5 0yju lpsm 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 frictionl .5b) fevfhn p7wp5ll6ess 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 pivotfhe7)l5wv bn fp6 l.5p. 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 rotate ayq7e.q f.t/c rbout 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 tangen.r7cqf e .tq/ytial speed of the center of mass about the pivot?

  06.24: A person tries to balance vertically each of three long uniua1h- gl5zy) j ao7g1rform cylinders wa)1 gya 1r5lguoz-hj7 ith equal radii 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, have masseem a8nbr(21l*hvur( ts $m_x$<$m_y$, 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 about a9j f*w gg;p5qin axis fixed through the center of the disk. Each disk is initially at rest. The radii of the g5gqp9jf*iw ; 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 massepbbrp fuh9bx *)g6: +as M but different radii such p:*b69b+ rxbf) p uahgthat $r_x< r_y$. 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 and radius R is pulled by a horon/x89 -eicwkizontal force F actii /n-koc8w e9xng
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.1mhjr0g8shpu 81y 2 q;y:xho wuu e1r of mass M and radius R rotates clockwise about its center ygu 0;81s. r1qpuhmw128j:oyu h hxe rwith 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 de8t: , qelb(x y.p css;d(+ayis 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 from equilibrium. When released, the cylinder rolls w,e 8qse(px:;+a dyb .scdyl(tithout 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 tb(.2gf9 xd.khhe3d .+ftk cnj urning in a clock wise direction with respect to the peh(2fdfbd. tjnx k.3h k.9g c+ilot. 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.