12.43: Several forcem5k(/t:k jj0q wr.3tu ypm1ivs act on a rigid body. If the resultant (net) force on the boru. pw35qt: y mi/mjj0(kk 1tvdy is zero, which one of the following statements must be true?

  97.39: A cylinder free to turoktp2i0f+i r5gc zp5/naround a fixed axis has a string wrapped around it as shown to the right. The string is pikpo2ic5gzp f 0rt5+/ulled 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 ans-p/(uzaud.+kzu b )w axis through its center. The stick starts from rest and rotates through wbpuzd/-k .uu+z sa( )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 ki4,p ifhu-32qrp6 oumrzh(u(vdn/qp: netic energy K when rotating with constant angular velocity. When the angular velocitduvr h6 q (m2/p zp4qf 3:r-p(u,unhoiy is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a flo9fja- :8(i6y)yurwj blq a7e nor 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 )wcwqb fv/t :0mass 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 and an ideal uniform ring ed,3l*,r 2k*mcfz ssehach have mass M and*2,zml hdk s s,ecr3*f 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 $μ_disk> μ_ring$.
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 unif(3 bdodob0dq +orm 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 3 +d (dbbodqo0the 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 cylind ib:x7k4.xbft dn0b(p er rolls without slipping 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 iti bb7kdfntx 40 .:px(b rolls up the incline?

  14.43: A long rod of length L is pivoted about its left end. It x *bw7ie6exe:qdp 8uev,thlm 2m07i 8is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod aboux8qp b*miee wuv,7 06dx hme7et8il2 :t the pivot when the rod is released?

  15.46: A uniform rod of mass M and length L is fixed to rotate about a frictien09z +0gbvi r,v eb-fonless 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 0e 0vrbz vn,-e f+gbi9of its center of mass?

  16.50: A uniform stick of mass M and length L is fixed to ro*aps 6m dt hmg.8wyefc12yz s4y:c x.p-v*px5 tate 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 clockwipp ye85xps-m*zd1 cs2 tv6 g4y.xa*wc f:.mh yse 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 js9m:- pd:wk teach of three long uniform cylinders with equal radii on th:wdst:-9pm k je 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, hc5)guc3 jqp*z/h:kr 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 mounted to r7m3qa u ;ygj mc zog-q)r:6vp3otate about an yqqzg -;7co m3gv6auj: m3 )rpaxis fixed through 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 difrnjszc 2ko:6) 8ha3jfferent radii such that)o:zfank3csr jh6 j82 $r_x< r_y$. 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 tj1t,u +xc. vp zz3iu/r,sn; vM and radius R is pulled by a horizontal rz, +v3 jtiv/cs;,1 .pzx nutuforce 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 clockwisgyju c(niwaz q6n9/5 6 g; :z,klbk:awe about its center with an angulakab6,lz9 kn/:cz:;qgu w n(6 gajw5iyr 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 cylis brgm0f5)b3 under of 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, strg 0r35b)mbfsu etching 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 of8q4zi*rhkw8iv8di sa6f 8dc ; 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 whsi av86 q8rw8cizkd dfi;84*h ich direction as the pilot tries to make a sharp lefthand turn.