12.43: Several forces act on a rigid body. If+pr udt5a6 y8 fn-io(tvh;dru 10 bn1)bja rt. the resultant (net) force on the body is zero, whichb(6dbt)ftdu1rhtnpajrn1i- a8 yruo+ ;5v 0. one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapped ar wv cngf.t (6lw3zp;wg 1zr/9qound it as shown to (r w9tnc6lz w1 pfwv/3.gzq;gthe right. The string is pulled with a force F equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick i p8 a.4zken5hi pkw9b6s fixed to rotate about an axis through its center. The stick starts fro8awzhn 5ibkpe64. p9km 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 fans5/g ; y2dr kz-ja58;ro4pp 6n5j7kfuashrl y blade has kinetic energy K when rotating with constant angular velocity. When the angular v;kf;a g6u/ jyjs yrz5olkr a7hnp p8s-d2r554elocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on wr7gbi ,o 0vv2a 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 rotational inertia p 0fh wq7g-/cxrhm u7;q r,u*d$0.5mr^{2}$ . 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 solih //7(vzc hs izw-pka*d disk and an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of friction fo-h pvhz7zi/(w*a c/skr 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 a 2n8te,jwy ega-pr02 pnd an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of friction for the disk and ring yn22er0 ptp8ew g ja-,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 plane.u8y*8o/.ndy i,w cnkc Which one of the followingw*/8o ku8 cyiynd. ,nc choices 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 about it vprjdjokg+(/y z+q:.s left end. It is released from an angle θo+vqpjdz/+y:r g(j. kabove the horizontal. 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 length L is fixed to rotate about a fk:y6iy -qry a1at4x.r rictionless 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. When the rod is horizontal, what is the magnitude of the tat:1-ya i4a r xykr.6yqngential acceleration of its center of mass?

  16.50: A uniform stix 3e1/ro2r*,n9e4)yuga zql h a3pvse ck of mass M and length L is fixed to rotate about a frictionless pivot located L/3 from one end. The stick is r l gp/ey),a x n23eqe9vr4os3*zah ur1eleased 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 about the pivot?

  06.24: A person tries to balanbr6px.w 8s rm)ce vertically each of three long uniform cylinders with equal radii on the end of hirx p8mw.6sr)bs 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,Xv -otvk e9coiqe-*0* f 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 mounn afu l694trrz .s,0mrted to rotate about an axis fixed through the center of the d,t9 60.un rfl4zs rmraisk. 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 d 5 tb8u51oujpeisks, X and Y, have equal masses M but different radii such t5epjuub 8o5 t1hat $r_x< r_y$. 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 Rizw s1h3b05qdsqfd3 dt.u9g 2 is pulled by a horizontal force F acting 2z.3i u9d dgwf0qbsshtdq1 53
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 rad j/6y.wgtxy- k3wp ap zvx6z42hc5 m/qius R rotates clockwise about its center with an anguj ap w6zk.hp2cy t4/z6 x5-/g3ywxq vmlar 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 r*fj *l (:cerjk xs7rga*a1dq3adius R=10.0 cm is connected about an axis through the center of the cylinder to a horizontal spring withqfj( dc:ga7 r*3 *sjkx*l ea1r 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 engin20w. l6ai4g +z iexzeqe 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 leftlz04 ax6iew geq+zi 2.hand turn.