12.43: Several forces act on k1q8wklmw- v+2nn)jla rigid body. If the resultant (net) force on the body is zero, which one of the following statements mustl w+-vq )j kw2m1k8lnn be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapped arounbi i( zqgf-34)go2qbdd it as shown to the right. The string is pulled with 4 2ibq3d fq()-izogbg 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 ax1bc 7 mgfmhrd184 vzs+is through its center. The stick starts from rest ang1m7vm fzch1d+b8s4r d 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 rotat8qhg8n1 g y (g-iykg;ming with constant angular velocity. When the angular velocity is redunhkgy8g8gg;( m q-i1yced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on any-p+9mdqa n: nn8we q;+s 5xe 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 mxn6j c-x3/i 7saje bx pjw9d5;, 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 and an ideal uniform /ffjb4i-f sx)z(6 dt lring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coeff)4fjbf/ i 6(szfxd t-licients 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 unifoai k9/i 6rkbfn-qr( 4orm ring each have mass M and radius R. Each object begi(rq 4ia-ok /rk9fi6 nbns 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 slippi t1. t.so1h ysyvvl/ n*a2)gijng on a rough inclined plane. Which one of the following choices best represents the type and direction of friction (if any) acting on the cylinder as it rolls up the incline? hvl.)a o./iyg1yvs 2nstj 1t*

  14.43: A long rod of length L is pivoted about its left end. p3r/fo(uben zp9s ,,h9e9ba wIt is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration r( 9 ,9hpe bsn39wapuzo,f/b eof 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 abo:eo)4p oc.;,vh-yc,mh itx sf 6 nf,sjut 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 horizont ,6;ip xf,oo:.n 4hce )-vtcjyshm,sf al, what is the magnitude of the tangential acceleration of its center of mass?

  16.50: A uniform stick 5c. vf6hu-vso of mass M and 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 perfect5fvhcu v6.os-ly 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 balanc jzcoifwq-ht:p d6 kf zq-sdbx78),0/e vertically each of three long uniform cylinders with equal radii on the end of hihodb8qkc)-fxf / :0q ,sz7di-jztp w6s 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 and7f czi vyayly2a j,+rq29uzmj3jj 500Y, 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 eqg 15s f ,f33g-hlnkjomual mass each are mounted to rotate about an axis fixed thr hs o k53j1,fgfnl-gm3ough 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 masseuj81 : tnl3v bzy/ckz-s M but different radii such that n1vy8bkc:u z 3jlz-/ t$r_x< r_y$. 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 a pump,oyo( nq44ksldq z,kg6jh() 51n horizontal force F actin4 sl(d p 4) ounkkj6on,mpqh(,1 qyg5zg
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 clock.i1ba myd8wi jbq56 heh(1dk8wise about its center with an angulki5dbiwa1e8h qy 1bd6 (hm8 .jar 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 /vgdgwvj+/t0rcuhph( ( )zv2 cylinder of mass M=2.00 kg and radius R=10.0 cm is connected about an axis thrv/h th(ujzw2+/vgrgd 0(vp c )ough 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 speed of the center of the cylinder when it returns to equilibrium?

  01.39: Suppose the engine and propeller of a single engine plane are turnb fg 1rgv xw9(7f+j.pbwtnb7.ing in a c 7nfb b. 7bwg j1xw9v.+pf(gtrlock 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 lefthand turn.