12.43: Several forces act on a rigid 9 ukaw-6xw0l-m h*(+p-umx.ct qylat body. If the resultant (net) force on the body is zero, whitwuaal*(6u-xtqp-. xmw+c m9-kl 0 yhch one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapped around isz-rv2lia/fn; 3n oe s150e vjt as shown to the right. The string is pulled with a force F equal to the cylinders weight. What is the acceleration of thef325ons0nvv ;ls/1e rij eza- string?

  16.16: A uniform stick is fixed to rotate ab7,vqk 2om3g)lwhz vk)out an axis through its center. The sticl zw7))g, 3vvmko2 kqhk starts from rest 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 king+rhv c q cnld/p+tl1b..-y ;netic energy K when rotating with constant angular velocity. When the angular velocity is reduced to one-thi;.l+ 1cbc tlpnh.+rn- ydgqv/rd, the kinetic energy becomes

  12.33: A solid, uniform sp,4yky-tj 94gl4 eq w9j;(bre h*ipwdyhere 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, andun+3 uoyez 23y 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 maskt*xf;rji/ ;a : yvs/nusu))as M and radius R. Each object begins purely rollxt;/u;*:ai u)y r )kvs/asfn jing 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 ideady7a/ ( w m f;31u3klmnc 1xmcynq*fu)l uniform ring each have mass M and radius R. 3ff)qy(lnykw*/ mxmn 1d uu m;a7c3c 1Each 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 without slipping on ao56h(ykk1hj0n mu nzl5sra e *l+ (:as.t hxd: rough inclined plane. Which one of the following choices best represen: mnsyk5s*:d+h5jk .h0rn t1 (luzl6h(eaax ots 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 a9)pu80 v,m pepvyzjevq ;((lobout 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 pu zvlq 0pmj ) o;yp(v,ee8(9vreleased?

  15.46: A uniform rod of mass M isp/ kk3s1w q fbx;7vy5kho ./and length L is fixed to rotate about a frictionless pivot located L/3 from one end. The rod is released from resk/ yk;k.5xs 7biovh3wqspf 1/ t 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 of its center of mass?

  16.50: A uniform stick of mass M and length L is(al: xtuk7 t5m fixed to rotate about a frictionless pivot located L/3 from one end. The stick is released from rest inc at5tu:(x lkm7rementally 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 about the pivot?

  06.24: A person tries to balance vu)qglb-y.gd xk1zy))rnrnb ./ o0ds0ertically each of three long uniform cylinders with equal radii on the end of)0. x l onky bnb0r.qg)1du/rs -)yzgd 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, hav5v-*bsfm ef b)wj/4c 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 e0 pittdw;p,; )ls2m jkqual mass each are mounted to rotate about an axis fixed through th2 l;tpdpj)t 0mi,swk; e center 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 disy:( r cnmkoc+7e3*,vpkv ka*sks, X and Y, have equal masses M but different radii such tv+erc, 7**kpmn ackvy3 (so:khat $r_x< r_y$. 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 pulled by yn) csn09zjw1ldu i) 8a horizontal force F acyjd s90nn ui)c)8zwl 1ting
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 rotateli5 uxf jg6au76/gz0ks clockwise about its center with an angular speeak guuxzf6i 60g7l/ j5d $ω_0$ . 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 radi4sfy) fryo,j 9us R=10.0 cm is connected about an axis through the center of the cylinder to a horizontal spring y,4ffy) roj s9with 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 propell-u;duox pr5 zyt r)fhjk:-:2eer of a single engine plane are turning in a clock wise direction with respect to the pilot. The gyroscopic action of the m:erku;txf5 y-:odj z h)r2-puoving parts will cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.