12.43: Several forces actv*f q4( dfsx+o0 ch8z zed;r1 ler9g.w on a rigid body. If the resultant (net) force on the body is zero, which(cfv ;srx0 d9fr1+h q*ezd4.owzleg8 one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a st e hr(ag. -qgjj*t4ee(g25qhfring wrapped around it as shown to the right. The string is pulled with a force F equal to the cyl.ae4q(gqgrhh t e*e52gjj(f-inders weight. What is the acceleration of the string?

  16.16: A uniform stick is yv0wq.l04 +yze wi1wd7l0eh4dxr dg7fixed to rotate about an axis through its center. The stick starts r1di0vdwq+0ey zx l. 47gw70wl h4dyefrom 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 kinetic energy K when rotatin(e;if+6mp(;:4 , (bq*)anz jptcfo ltyl mkidg with constant angular velocity. When the angular vea, (6 4intf)qkpbdml ;(*( mytjc;:+ zeioflp locity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphereh oa: xy(i:z)u 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,im-2 2av .sif (gvb6vo 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 id7a,r 90tlh jnq:ta cl0g9va1a eal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The c :ja hntl09cavr,1aq07glat9 oefficients 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 ub)sg jyb1pwv k,n 8y.0niform ring each have mass M and radius R. Each object bpkj8.w1bb )gv0n,yy s egins 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 a rough inclined plag c,up1viio; 6 r(ij/y6 *spocne. Which one of the following choices best represents the type and direction of friction (if any) acting on the cylinder as p*viu6,or ci;i6 1sc (/po ygjit rolls up the incline?

  14.43: A long rod of length L is pivoted about its left end. It is rele tpmnp60 jv l2n)kb/4based from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pivotbl02v j /nt6bkpmp4n) when the rod is released?

  15.46: A uniform rod of mass M and length L is toq vspjv h v(by09c7hyh2p*nz4e/8 / fixed to rotate about a frictionless pivoz4q vh9tbchny/vys*phe oj 7/20(8 vpt 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 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 aqkl,gbc7lf io.4n0tcu ujy , x7,68un 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 i b 6nj ,gknc,7uouyq lt 7fi8uc.xl40,ts 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 vertically each of three long unifobai) +khco:k f3dk4 3m e(a9serm cylinders with equale)c9: dko a33miak4k f e(h+sb 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 disk onlgsc : k.zqyfn83*2s,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 ; tqy* zo,.tf qge3z)requal mass each are mounted to rotate about an axis fixed tt.o) y z;r3f *qegt,zqhrough the 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 disks, X and Y, have equal masses M but di 5ze 6(s97 9pegcx7s-d m ycso2y5gxgefferent radii such g5 2ge7yx69c m oe9psc(dzyssgx 57 e-that $r_x< r_y$. 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 m la2 yo+f8xno*bp4js/ass M and radius R is pulled by a horizontal force F actinp/o fl a*yjsno+4xb82g
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 rota)u *6 /bwek,xj a/mlewtes clockwise about its center with an angular speed jxe/m/ ,l*k6euw w)ab$ω_0$ . 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 fp8efjz m -o11x0b0vcnpq2ht.z5 d jv 1yu4g6mass M=2.00 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. When released, the cylinder rollq-j. ofnpfex25 h 1zgy 4vzmtd 681c0pjvb01 us without slipping. What is the speed of the center of the cylinder when it returns to equilibrium?

  01.39: Suppose the enginx)sk3:+ ieq bge 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 pi b x+k)3esqi:glot tries to make a sharp lefthand turn.