12.43: Several forces act on a rigid body. If the resultant (net) force )4kro m2.dr s. ih4lvl1w8cgaon the body is zero, which one of the following stateha.) w8os2.i 4vr r4d 1lcmlgkments must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapped arou4ibmq l7f9vw*s.w9wazfn 5 +und it as shown to th9iv5 f wz9+*.wmqflb 7usa4wne 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 is fixed to rotate about an axis through its centerrfpi58d)m3gw6) 7q nmvj hye9. The stick starts from rest and rotates througvnw 7f)i r)j q3h6mgd5p em98yh 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 en)4gybr5ydq9 ;vz ai:y ergy K when rotating with constant angular velocity. When the yd y:rziva9y5 b;gq4 )angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere roq(ezz7 e,o.y clls 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 4m q9gk7pss*sfg+/ qg 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 z9a8 wt0qck8 eeach have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of friction for the d8qwae ct k98z0isk 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 dis-653u ikqfdqvfmi7cr ptr.oid8f-. .k 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 for the disk and ring with the incli pd c -i.qidfm6r7r o.f-f853 qvt.kuine 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 withoq6a/ u+(n 6v;u gshopcut slipping on a rough inclined plane. Which one of the f6qp+ /;(g6s uaoc nvhuollowing 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 its left e*buy ) u-4bqs y/dkdte4*d ts-nd. It is released from a) /k4 4t* eydsqbyusd*-u-dtbn angle θabove 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 fri/ r- (pkrkg i,2xtncq-+6k e8xx/eltkctionless 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 ce glr-//nt+i68 ep- t2(rcxe kxqk,xkk nter of mass?

  16.50: A uniform stick of mass M and length L is fixed tr( u50 w):qfe-ayrymv 1ju8qzo 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 sticr yq:8uz-1)u0(qmwj r5 eyfavk 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 uniform cjh3cx7t m 5c) 5f 5j;/c,rnyzxrk glh5ylinders with equal radii on the e) h5xczg53;r k7r /m5jxc5hycl tfn,jnd 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, havq3j vu )jffnyrgng/)yn5 d5,.4;kn soe 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 m(1* kko9 k:wbpbss6dp1+h jnaounted to rotate about an axis fixed through the center of the diskdwk as1j ks9k*o+b1h(np pb:6. 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, tu v,vd9u*g k3have equal masses M but different radii such thatkv3g9t,vud *u $r_x< r_y$. 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 mspng,- uyo+t :0 ;jckvass M and radius R is pulled by a horizontal force ,n sg;0ytvkjo:+-pc u 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 mass M and radius R rotates clockwise about ,ba w 3cb8wz8/-pdkrze3)kqrz i 3f1 lits center with an angular speed 38lwb ebp3,z w rc)iqz 3-8rk k/fdaz1$ω_0$ . 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 o2((dt)*-qkin:en jdzct 1 yld:gs0 nvf mass 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 rolls without slipping. What is the 0i(q n t:ykl ndv1)j d:tcsge2*zdn(- speed of the center of the cylinder when it returns to equilibrium?

  01.39: Suppose the engj.;/gu ztj z5s0ob1 j+ o4dq:b sig/xwine and propeller of a single engine plane are turning in a clock wise direction with respjx /wz+;qtdb1o: gb.jzus0 /ojgi s45ect 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.