12.43: Several forces act on a rigid body. If the resultant (net)5 :b2i.sodubx force on the bodyisudb5ob2.: x is zero, which one of the following statements must be true?

  97.39: A cylinder free to turnarosebr -j:1k7 wk* vw*vvund a fixed axis has a string wrapped around it as shown to the right. The string is pulled wi*:*-jwv7sk1v bwve krth a force F equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axisq6n7akk f9vcd7,s fe gj w);z- through its center. The stick starts from rest afn ,cz7 6)q7sj ekfwg;9vk-da nd 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 kingj(gz0 awtr ,2bb.k )yetic energy K when rotating with constant angular velocity. When the angular velociwb,g2y jr)zgab t0.( kty is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on mhxy zy4exk9:g(:5w/d nwbj; 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 mass9.iozg)q9 d or x/k5rz9q k6rr m, radius 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 an:w 5on ( ckod;hao4tsi.qc 05rd 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 with the incline are dn;:tho 4(. oari55owskc q c0 $μ_disk> μ_ring$.
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 7cf, wz sawjw+ ugbm9h-5. v32.kjfqean 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 with the incline ars3 e5wc+fk9fw7g b , .hwquv.2jzaj-m e $μ_disk> μ_ring$.
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 rougbo1 vlj3-b 8dsh inclined plane. Which one of the following choices best represents tbjb3vd l18 o-she type and direction of friction (if any) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of length 71na te27kajs) b 9.ttpkz8ygL is pivoted about its left end. It is released from an angle θabove the horizontal. What i ye2p. zbnsg7 78a1ttak9jtk)s 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 evmn08)sk o7tfixed to 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 rotating clockwise about the pivot. When the rod is horizontal, what is the magnitude of the tangential acceleration of its k7v8e tm)o0sncenter of mass?

  16.50: A uniform stick of mass M and 1 /t7jer 8pdlhydn46q:tffb* 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, resul7l4e6 jtb1f/np8hd* :rt fdy qting 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 vertically each of three long unif b2)cykp( pcl1rp3 (xbm,dsp4 dtb2h5orm cylinders with equal radii o (4k3php2 )d, ptrcsybb(cbp x1m5dl 2n 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, have mal6(amx qn5v t7sses $m_x$<$m_y$, 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 dmpqp5*0 3 q;h tftu::lq qfffks(7(y an axis fixed through the center of the disk. Each disk is initially at rest. The fp(3q::uy th f tq7dfskfq;0 5(*plm qradii 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 v qukb - 8d/4(akjte4fdifferent radii such th(u4-taj kekq/fb8 vd4 at $r_x< r_y$. 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 pullx sffcyk +d9fnt)3fupf4.9r /ed by a horizontal force f cfd+ )pr/ ff yfs39x.49ktunF 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 and radius R rotates clockwise y m6f edb4om6*about its cent mdbf4 o*mye66er with an 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 cylinder of mass M=2.00 y 57zmxxggvp6 d,f8b4 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 revg8yz xx76 bdmgf,p45leased, 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 7/ yjg s,xrp;ypropeller of a single engine plane are turning in a clock wise direction wit/rgsxy,y; 7pjh 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 lefthand turn.