12.43: Several forces act on a rigid body. If the resnh2a sxj2gc8:f c1nb 6dci5c;ultant (net) force on the body is zero, which one of the following statem i cf152nchdnja2x;8 cg6:scbents must be true?

  97.39: A cylinder free to turna ue+-gg3syvpo5;cc2o w) 7clhround a fixed axis has a string wrapped around it as shown to the right. The string is pulled with a force F equal to thee53 yl-o;ucgp sh7gvcc)o2+ w cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about-ho x(s9xmpl3 9z g1cq an axis through its center. The stick starts from rest and rotates throughchopzs9 x9 (3gl1-m xq 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 rotating25: cbh; xrfvqgy6obb tgt k25ot( 7y6 with constant angular velocity. When the angular velocity is reduced to one-third, t 5bt rk2 h y62(ob;oqgbft5v6 g:yxct7he kinetic energy becomes

  12.33: A solid, uniform sphe9: milfn f9jw(re 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, radiuva lnvz1m* 2b9s 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 mass 7+0ma1z pw/ b 5loewuoM and rad1 ozp bm7ow+w5 ua0e/lius R. Each 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 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 idealpp:4kt8 uxc+jbtimdl .21ue , uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The84kt1:pdtlu ,2.xm ibej+ ucp 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 roll.hgfybu,v)pxpx / n wb.3+i0b s without slipping on a rough inclined plane. Which one of the following choices best represents t i)ybvb.g3nx .fu+pbpw,0xh/ he 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 pivote :rktaxid5, m2d about 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 rod is relea5,txikmr 2:adsed?

  15.46: A uniform rod of mass M and length L is fixed g qrs323spwirdix3 6u3 8 xu*mto 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 rotating3 iq38p3*g6r 2i srxud3xu swm clockwise about the pivot. 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-fvwwqea0c m c3 7j8.pc38hgy 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 ofema3 f hyg.- 30wpcj8wq8cv 7c mass about the pivot?

  06.24: A person tries to balance vertically each o0sdt-y1cdr0 jo2nmboj7 6e : xf three long uniform cylinders with equal rayrcodjnex1d 2:mts0o7j-b 60 dii 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 andY, hac;/1 a +obt immn.hop ;u.le88fwbsdsh5f(*p ve 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 about g; r56lph(acvan axis fixed through the center of the disk. Each disk is initially atgplv56a ( ;hcr 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 masses M but diffek e. d:/vukpt4ksy0w8 z:q wt)cr6uw /rent radii such thaw.rt 0/k kwev d : wu6)4qypztk8/cs:ut $r_x< r_y$. 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 iseuwpjn1to(4i1 ym9 n o6jf9v0 pulled by a horizou96e0( j9 vt npinj1o yomwf14ntal 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 masv .pph*3qb/( dcfdmatd a0,nhp8p6 )zs M and radius R rotates clockwise about its center with an angulart 8(a.hqfzhd)bacp3 d p/mpdvn*,0p6 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=2.0/ u)5 azlfaff20 kg and 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 1.00 m from equilibrium. Wheflz/25u )faf an 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 prop3sv d,fbz6 qm-gufn) s p)x lol,28ob6eller 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 shm8)zlo s,b6 ,dnbq)fo -lu6vpx g3 2sfarp lefthand turn.