12.43: Several forces act on a rigid body. If the rezw/.wagx+ajbleous73 9 8z7asultant (net) force on the body is zero, which one of the following statements must beuoga w +7.xb8j/ 9l7zw3 sazae true?

  97.39: A cylinder free to turnaround a m l *ukryn*.phy y/5k( m.ox+tfixed axis has a string wrapped around it as shoo5x* mk.yk+* .pyh(yuntmrl/ wn to 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 about an axis through itskr)e+9 5e fmwq center. The stick starts from rest and rotates through + m5r )fqkewe9an 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 e)t,sv gy +pdqi5csnn6/ .bydtr;5y g -nergy K when rotating with constant angular vey+5r )ns6y;,yqt/p v .5dbgn s-dgt iclocity. When the angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniforb5a 8. cuqdur6m sphere 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 inob; jgtzjv w.p5p -..nertia $0.5mr^{2}$ . 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 n 4w ;.b ..ang:.bltwh.iynkd each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined i n ;gbn.kwdht...w:l nyab4. 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 m 7+yykabyv 1y7ass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficient+kay7yv71b yys 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 inclinivk2d g 3teg1 ( anulrq3+b 93.6iqigned plane. Which one of the following choices best represents the type and direction of friction (if any) acting on the cylinder as it rolls up the incline iq.eg1vu(3 ig+3 r 93ag btn6q2lkdin?

  14.43: A long rod of length L is pivoted about its left end. It is releasexa/t4v4-np q4ulf m;u+x5 cwl d from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pivot when the nc-x pq4w/ 4lmafl v5uxt4+u ;rod is released?

  15.46: A uniform rod of massj4tcd3 vl.ao9 m*2km u M and length L is fixed to rotate about a frictionless pivot located L/3 from one end. The rod is released from rest incrementally a.ma3cm *j94dl vk2to uway 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 rotate about a frictp6x.6 su*ucxe)ma gg/ z0 t6uqionless pivot located L/3 from one end. )seg q/m0u6ux u* a.tpc6xg z6The 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 tangential speed of the center of mass about the pivot?

  06.24: A person tries to balance vertically each ofdf,5qpgsu (-u three long uniform cylinders with equal radii on the end of hi g-5(uspqfu,d s 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 masses 4/y.5cmi yv;65rouig(af4 epk lg8 pf $m_x$<$m_y$, 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 v*u:( ch6r9l4 ovtmruabout an axis fixed through the center of the disk. Each disk is initially at rest. The radiior 96ctvruhm4v( :*ul 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, have equal ejdt 0puw)ce-/+t7 tq masses M but different radii such u/p)t +t-e qjc etdw07that $r_x< r_y$. 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 hor2l,bce064 fyd-ye drd izontal forcl2-cb e6rfdy dedy04 ,e 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 )8d6e i:q*5xe gc2boehg4 xf9c7t drdits center with an angular sp )gcrqiogf592 6hede xed*78c:tdx4b eed $ω_0$ . 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 conne3s9e1c/fls zjcted 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 releases le3zj 91s/fcd, the cylinder rolls without slipping. What is the speed of the center of the cylinder when it returns to equilibrium?

  01.39: Suppose the enginxrvqj flsy7dq /;(,y 5e and propeller 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 plane to move in which direction as thlyf qd r/yx;vs57j( ,qe pilot tries to make a sharp lefthand turn.