12.43: Several forces act on a rigid body. If the resultant (net) force on thexs cqm/jw5x, 1/k/nbe body is zero, which one of the following statements must k,b xwmncq/x/e5js1 /be true?

  97.39: A cylinder free to turnaround a fix8 7e j+aslmuo2+rmhn6ed 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 ac j7msnl +r2e8uam 6+ohceleration of the string?

  16.16: A uniform stick is05w, g1tlzo m )hruc-q fixed to rotate about an axis through its center. The stircq5t,muz h 1g0lo-)wck starts from rest 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 bladazv cj)( al;srj+n5+z o32rety.c m+ke has kinetic energy K when rotating with constant angular velocity. When the angular velocity is reduced to one-third, the kinec( aly;j+) o.vr+c2jenrtm5zzk+a3stic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor al0,oo 8fkf u2ef ca,x*jo9pbo/ong 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 rhh cwg k)y( +4kayi-:iotational 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 uniformu8(-s0,k2n krui ssmh ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coeffici0hus28 mkk(,ns rs-uients 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 ha8 v(ocf6b (hdlve mass M and radius R. Each object begins purely rohd c6f (ovl8b(lling 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 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 wit )3do vs9itde2hout slipping on a rough inclined plane. Which one of the following choices best represents the type and direction of friction (if 23dest) iv 9odany) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of length L is pivoted about its left end.9ks, -oqd*nb m bnrzp,w:+ ho8 It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pik :mb- ns,,b*o +r8qwd9zh ponvot when the rod is released?

  15.46: A uniform rod of mass bo+b+m8qc b sra /8)elM and length L is fixed to rotate about a frictionless pivot located L/3 from one end. The roao+ce m)8l b+8sb r/qbd 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 center of mass?

  16.50: A uniform stick of mass3/jck ,; phqhb 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 ihpb/k;, 3c jhqs the tangential speed of the center of mass about the pivot?

  06.24: A person tries to balance vertically each of threikv si**.qalw; f)cw7 e long uniform cylinders with e;*qv).wswiikc fal 7* qual 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 m4aic plkusxup2/0o ; zin .4/aasses $m_x$<$m_y$, 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 mou: i9wc flhtt0c l02/qs4y/na) 9t ykwtnted to rotate about an axis aqiwfty9ylc0h2 /st tl)wn/9kt4c0: fixed through the center of the 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 andcnjdu-q d bko,,1w s:1sgp 3nr et/:1w Y, have equal masses M but different radii such thatwk-1de pt n3:1 qncgswdu:rj obs,/,1 $r_x< r_y$. 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, solidpvf1zrpwu m1cm4+ r6/ cylinder with a mass M and radius R is pulled by a horizrp+1m / vcmfzwp r41u6ontal 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 rota am:.dfgzt*6wkh hw 6*tes clockwise about its center with an angular d.6wa*gmkh6 wz:h* ftspeed $ω_0$ . 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 c1dxy x4)gzpcr0 kf,zi dbw9)5ylinder of mass M=2.00 kg and radius R=10.0 cm is 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 roll)01,g w5p )b4x cfiydzk9zrxd s 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 a single engine plane are tug)3 hw;svb sbx9uu9p -rning in a clock wise digub-hs99pbvux3s;) w rection 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.