12.43: Several forces act on a rigid body. If the resultant (net) force onz d uz 2s)wnxra7 7,0ut3dfze+ the body is zero, which one of thee n ,r0tz7az73)w uzsdx2u +fd following statements must be true?

  97.39: A cylinder free to turnarek+qrui b :-8xound 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 acceleration o-eu br kxq8:+if the string?

  16.16: A uniform stick is fixed to rotate about an axis through its ce,v7c8a bur:dunter. The stick starts from rest and rotatesab urv7d,c8u: 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 8:i..tov2ul mwij5mq energy K when rotating with constant angular velocity. When the angular velocity is reduced to one-third, the kinetic energy becom..mto2 m l:qi5u8 ivwjes

  12.33: A solid, unifyoir, 6wm 5xre-d, fs9orm 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 rotationa(+z bcl7t rc.nf5 uf(sl 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 idea x26(00 zbjniytw3f- nnhle(sl uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficie slw(ny20(etj6fx iz bnh3n-0nts 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 mass M a0 v x lz3fs wlso8+f3;hs+t*lbnd radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficienf zsls3l w+xsofl +v0b; t8*h3ts 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 wi-+cm o: n9xmbs* /kofbfo9h/8b k.gizthout slipping on a rough inclined plane. Which one of the following choice*/.9m xhok mf-:b9+c bzbo ni 8ogkfs/s best represents the type 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 abou 5tjqedh5 h 9r)* ;fve k(xg6ya,qh:uhqo17zjt its left end. It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration)ruf ,h *k 5jt;hog5 xh qa7y1d:v9zj(qeeh q6 of the rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M and length L is fixed to rotate az a-bm-/kvj0ot)x5 ( v xp(llxbout 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 jvt/l(-xpom)(k0 z-vlabx 5xpivot. 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 3)v843 y bemlcac:sudM and length L is 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 speed of the center of mass abo:av34 8blscyeduc)m 3ut the pivot?

  06.24: A person tries to balance vertically each of three lon: qg.c m 08ohnenn02szg uniform cylindersnzo 0sn2 e cq:n8mh0g. with equal 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 di s)qu emdi y5p9mxv;5fa;61ugsks,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 mok uz msx :6ozaf0sk.s 74aim)/hoo 1,lunted to rotate about an axis fixed through the cen0ook.ssx:zmiaflu) mk1a/ ,6so7 z 4 hter of the disk. Each 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 eva( /j.l puc6pjqwrl0a(2*y 0hqg0h fqual masses M but different radii such t cq*0(2fljrp guvpl6a0 ./q a0 y(jhhwhat $r_x< r_y$. 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 - l:u pnr.u,au5f:soin+pzb1zq2 ul,M and radius R is pulled by a horizontal force usaf5n u.lnl2 qz 1 +u,p-p::uozrb, iF 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 andx:3dt :-eog )npntxr9 radius R rotates clockwise about its center with ar td:nx9g- )xpeotn3:n 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 cylindq*uj79jae:* g hewdj7 er of mass M=2.00 kg and radius R=10.0 cm is connected about an axis throu77udjhjqaw *gj* ee9:gh 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 is the speed of the center of the cylinder when it returns to equilibrium?

  01.39: Suppose the engine jwov38f3c: qg 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 the pilot tries to make a sharp lq3vgwc8 3f:joefthand turn.