12.43: Several forces act ounu7*(a2c4dwxy m: xbn a rigid body. If the resultant (net) force on the body is zero, which one of the following x4*nu( bxc7y a:2wu dmstatements must be true?

  97.39: A cylinder free to turnaround a f sr8eu sg04l ))dq*t cfcgm3e*ixed 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 gldsm8u43t)rf eg) s*q*c0ceacceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis through its cl y44k a)b/s6xbzcvv -enter. The stick starts from rest 4a- clv/6vxzbb4s) y k 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 ki1 fl.ruk7z /pinetic energy K when rotating with constant angular velocity. When the angular velocity is ki. pr/f 7uzl1reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipps3 pdcw:0 4:qfdhs8l cing 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 maeyfn-*/gjnff) f; )at ss m, radius 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 have m(yv) .n xkq g14;6afxlb ,zydtf- mol7ass 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 the in 7q; -( ydtgl1nzf4k6yxla,)xmbov f .cline 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 s*h oz:jk b q+:ia5m4rbolid disk and an 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:a:*b4hz + bi5qkrj mo 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 rgxmj;bva d4 v8mn 4;uf 8/wc7inclined plane. Which one of the following choices best represents the type and direction of frict4 8dx mvr;48 njbvwa7;c/mf ugion (if any) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of length L is pivoted about its left endaf c4 h zioub+9j5d66.xuz8zq . It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pbjz6 u8 9z .6+czho5fd4iuqaxivot when the rod is released?

  15.46: A uniform rod of ma,sagkz):p ;yhs 23o,o w dt0fiss 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 away from being perfectly vertical, resulting in the rod rotating clockwise about the pivot. When the rod is hori yto;god,fi:ssz)k 0 3wah,2pzontal, 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 vufb ypqd6tvr.( l;dm+1( w,m 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 spee(dm (vwf,pq.tmu; 6b 1rly+dv d of the center of mass about the pivot?

  06.24: A person tries to balance vertically each of three long unz7l;8 dkjgvj7nr6iox4:j 2xx2p -li d0y hw 5qiform cylinders with equal radii on the end ofk-x;yzx :4d0vpjjridl72qw 27l85 xno 6hj gi 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, hav,cuf)1ijx5y;sin ik in ne/**xa j,s1e 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 unifoqg :gra+ex6e*-d;q d wrm disks of equal mass each are mounted to rotate about an axis fixed through the center of the disk. Each disk is initial xee a rwg+qg-6q:;d*dly 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 equzqlz 9jkvb.mw /3 :tww (tv(j80f)j gsal masses M but different radii such that/j (jsvm8:q vwzf t() z.3b9lk0gwwjt $r_x< r_y$. 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, soli/y cx,jo 5(xvbd cylinder with a mass M and radius R is pulled by a horizont 5yo/,xxvjbc (al 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 mmi:uoh qt bqo:t*ll0+9n4 i 7and radius R rotates clockwise about its center with an angul9qq t 0*nmhu: mlb7:ioo+i4l tar 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 sol6+zzs)k)l i peid cylinder of mass M=2.00 kg and radius R=10.0 cm is connected about an axis through the center of thz 6ipse+l ))kze 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 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 8)n6gfo/tiz*ha q:bl 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 dire/fl 8z n 6io:*ahtb)qgction as the pilot tries to make a sharp lefthand turn.