12.43: Several forces act on a rigid awo +tf/h:o1bbody. If the resultant (net) force on the bbw1fa/ot + o:hody is zero, which one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has acco*1r9j1tftht 7w8ze o1p* x6f 9jxj 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 acceleration of the stw9o x1 67jf *erzct o8t1 c1x9fpjthj*ring?

  16.16: A uniform stick is fixed to rotate about an axl)dp ;mj0;z) fy,l7 ydqmcg,wis through its center. The stick starts from rest and rotates thr;,;mzd0)py,mylcl7 ) j gfqwdough 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 rotg9l/y -3 q zjyr5 yspgloj5 n/:ihu-(vating with constant angular velocity. When the agl 3onr uv/-jq:s5 j yhl9i/(ygpz y5-ngular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls04oq9f:bew q) k37;l omr,umqu4wm dn 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 m l-s/;cy jmn5kass 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 rinn uie9h, 54; s8er7e zb:uzbwcg each have mass M and radius R. Each object begins purely rolling without slipp,cz ueun5b:h ib7 ;e9wes8r4zing 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 ) .rh9m5vifvrm- 2jbk2h h( budisk and an ideal uniform ring each have mass M and radius R. Eahjv.mk b( 2h2rbu -5 vhi9rfm)ch object begins 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 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 withoutyoc(8g tt2 x1d slipping on a rough inclined plane. Which one of the following choices best represents the type and direction of friction (if anycg o(tx 2y8d1t) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of length L is l 5o80ucbp)iwb9cg bwq6xc)9r5o58zmu( bpj pivoted about its left end. It is released from an angle θabove the horiw5i6j5ubo)89lbp(m)9xqgo0 p bc bu 8c r5zcwzontal. 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 and lekyly8 o+ vf689c2 -jecvup cf:ngth 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. Whe cf28uyccpe -o6k+ j8:l9v fvyn 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 frictiq8p73en..armal)sc0c d 3b ewonless 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 speed of theem3cl dawa..7 )0re3bsq8pc n center of mass about the pivot?

  06.24: A person triesp0smv k/cj ,,6ux r-bo to balance vertically each of three long uniform cylinders with equal rar,,mbsj 0 uo6/vxpk-cdii 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 andv, ho(j 6dhl5yY, 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 arclyz6v *ei zdzuk1n3 7fv i.ext1*,c2e mounted to rotate about an axis fixed through the center of the disk. Each disk is initially at rest. The radii of the disks ariy16ntv ,fl.zc7ixcv2eu1**3 d zkeze $r_1 < r_2$. 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 equaswbv(d8 5dg8,/anu rpl masses M but different radii such tg8v r(p/dbw8 ,5nad suhat $r_x< r_y$. 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 /qrvgtf(zc;7 ,0bv zx cylinder with a mass M and radius R is pulled by a horizontal force F avgf z0zct ;q, br7vx(/cting
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 dis cq/(xaj8.z ndk of mass M and radius R rotates clockwise about its center with an angulzd/x.jca q(8n ar 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 o8qm; x4hpx tzlo )a)7R=10.0 cm is connected about an axis through the center of the cylinder to a horizontal spring with 7zx)px mqt)aohl4;o 8 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 plane are t7 tti baro8, v9z;dej*urning 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 pilot7 vtdzo; it9,*era jb8 tries to make a sharp lefthand turn.