12.43: Several forces act on a rigid bo 87d huz2h u2u8;8ynwm stl3hhdy. If the resultant (net) force on the body is zero, which one of the following stas2huuh8hu7w h8nz3y8dt; m2l tements must be true?

  97.39: A cylinder free to tur/ uywe,l3wjlq : 2i+es7dv h-m*xu qs.naround a fixed 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 acceleratus:wxhilyq-32u.l *m7j + eswq/,vedion of the string?

  16.16: A uniform stick is fixed to rotate about an axis through its ls3vm4ej b). kcenter. The stick starts from rest and rot svl4b3 m)jek.ates 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 whenh cle/.2ax:hk,pwy4mxo u,2l l 3m;ek rotating with constant angular velocity. When the angular velocity is reduced to one-third, the kinetic energy becomw x 3l,l;o:ypm eu,xelh.c k24/h2km aes

  12.33: A solid, uniform sphere rolls withlk(d .sjlbn y qet5;q58w;9l3nd fu. vout 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, rad)e7 io7s-bllb ius 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 hzoodu 7 /lx3b;ave mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. buxz do 7/;lo3 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(jseb*, o0x-2tqsp cg ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of friction for the disk and ring with ths j0ec - (sqx,t2opgb*e 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 inclined plan8u2 mm 9zzpu(ttmyg4os02lo 5e. Which one of the following choices best represents the type4yoz9l m0pmzt (ugst2uo2 5 8m and direction of friction (if any) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of length L is pivoted abok 2c.-j/n n be-uq:sntut its left end. It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pivot when the ro/qeu-- . tn:n2sbcnkj d is released?

  15.46: A uniform rod of mass M and l0ah2hx7 yo am*fd) e5pength 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 pivot. When the rod is horizontal, what is the magnitude of the tangential acceleration o ox75aa0y*mph 2)f hedf its center of mass?

  16.50: A uniform stick of mass M and length L x,k: c2u( yhsois fixed to rotate about a frictionless pivot located L/3 from one end. The stick is released from rest incrementally away hu os,cx(y k2: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 of threvs 6w 2bax::l ;cy niwcv-y2)qlv+x; me long uniform cylinders with equal radii on the end of : mly; alq)xi+bw6c;vwx:-vncv2s y2his 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 di qy:s1kilw4 b/sks,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 rotate abo5 f*qju)wk u km3ugvzu8ao)49 ut an axis fixed through the center of the disk. Eachoj zqugumkvau)3kfw5) u89*4 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 and Y, have equal ywl 4sg.hbhtsd/l3 u349jim9masses M but different radii such that s4 3wg4d3.9u/il 9mljythhs b$r_x< r_y$. 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 pulled4(7xc*q brsgk by a horizontc7x*gr (q4skbal 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 csupi/d/ +s16hstt c n9lockwise about its center with a 6//ischns ps+u1t t9dn 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 an+.qd b/ /lia fwhf+o+wrfc;/ rd 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 1d/ w+l ffwr c ./qi;rfh/b+oa+.00 m from equilibrium. When released, the cylinder rolls 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 turning1 ,*vy -lf h9 zwdzvobf.f(bs5 in a clock wise direction with respect to the pilot. The gyroscopic action of the moving parts will v1,slffdzwv* (.f yb bz9 h-5ocause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.