12.43: Several forces act on a rigid body. If the resuloxrr q 9ijgk3c/4-e1tvxl.;d* aix e/llz /d*tant (net) force on the body is zeglel; * oiqivx ldx3r k/d*t/acex.z1r9j4/-ro, which one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapped around i)tx x ;j(ivkhpif,l+ /t as i/tk ixp+,)hjx;f(l vshown 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 itsrr 7sb7g2/x*pbf as n3 center. The stick starts from rer 72r7p xg/a*s3bf nbsst 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 energy K when rotating with constant anwyw8m9d(alo; jln867,*fc gf cxmn:ggular velocity. When the angular velocity is reduced to one-third, the ki nw (f:ma7 8 m6ycldwg8xc *gflnoj;9,netic energy becomes

  12.33: A solid, uniform sphere rolls wih.6 mvk.t.t sithout 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, rad1uaq5t xa4n :k+- nkldius 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 un cmik fy35r,*q pl3x4hiform ring each have mass M and radius R. Each object bkxi3m,l4 q3hfr ypc* 5egins 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 an ideal uniform ring each have mas7 cgpa4)o el7nk30sig s M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of friction for the dis 7e cin7psggko4)3 a0lk 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 rollq (lyfk/a;ma3zyphj *21c x6qs without slipping on a rough inclined 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 inclinzq*yq1263fy h l;kxaamc( j p/e?

  14.43: A long rod of length L is pivoted about its left end. It is releasezs4+9h/.5 xr h (8gztkd vufsbd from an angle θabove the horizontav.xzzssrg95/8k4fbd hh (t + ul. 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(w8alu58htz 6jjw.x.ddr em 9 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 pivjl wu6h .88t(.wmd9zerd j 5xaot. 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 x2zi4lcq ; 2p(.agsif 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 the tangential sxiz2lf.c sga(q 24p; ipeed of the center of mass about the pivot?

  06.24: A person tries to balance vertically each of three long uniform cyxa/9587acxjbwg t ;e 9pxsn 4xlinders with equal5ga/px wxxsbx 8a9 7j4ec 9;tn 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 diskp3c/sta93dg* .-ld bj/ imj:rk 8o dbss,X andY, 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 mounted to r,:vz)nvdua u;-ir 0 rc u(,lesotate about an axis fixed through the center of the disk. Each disk is initially at rest. The radii of theiz n);vr0u,u:scvlr, -d(a u e 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,a56db 0eiok:mzvd /jfn ; 6x/h have equal masses M but different radii such thati6/; jenzvx/:0db5ok 6 hfm ad $r_x< r_y$. 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 wi- 41yeic gdqdbgdc9 9+th a mass M and radius R is pulled by a horizontal force F 491i gd c-ecbygd9 +dqacting
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 ri,0*hows vfve2ye5:symqc 7v. /8 rea adius R rotates clockwise about its center with an angqyr e v 7ch,8e*m/ae0s yvwvi.:s52foular 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 crv;5v q. ynj 1 l,.v ,i7u.gh9ejgslnrm 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 rolls without slipping. What in95qr 1.v;hivy.gsj .reujlg7n l, , vs 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 2sf281cfxoop 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 the pilot tries to make a sharp2 8fcfso2xp1 o lefthand turn.