12.43: Several forces act on a qo1e,hlu /4z crigid body. If the resultant (net) force on the body is zero, which one o c/u4 e,o1hlqzf the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a streurogz+.fgl3 ;9is,t- 8a gylb,h c;zing wrapped around it as shown to the right. The strin afe;g3o8 slb.9h,c z+-gi u zygt,;rlg is pulled with a force F equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick i: 4 bejqq5xl 8ho;l ow8k2ui*ms fixed to rotate about an axis through its center. The stick starwleboimu:q2lj x; * 88o54hkqts from 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 fan blade has kinetic enswb(l1y sa:+ zergy K when rotating with constant angular velocity. When the angular velocity is reduced to one-third, t ba +s(:wzy1slhe kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a u:+ h jf-riene .gfnqi0 b0k8,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 hphni6v/zx6g5.v7 acr as mass 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 xh3avd9 70g nmrt6/ +0(taqkk,lllp ddisk 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 anlp/7tn 9 (xg,rklhdvqtd06 a 3+0klmad 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 unifo huli,o;fp9i/rm ring each have mass M and radius R. Each object begins pu9ilohf,i ;pu/rely 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 slipping on a rough inclined pl- icb-z bl8x,zr4s7u)i4 7d/7qffx5 r nvfwolane. Which one of the following choices besfub)74i5z87r l/dwxxo l-svb qf7zi- r,f 4nct 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 at igfq./n(+ae bout its left end. It is released from an angle θabove the horizontal. Wha+.ign /qtf(a et 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 leng c ((mngkqzu1qi j5 ulmi3o wp33p0)7lth L is fixed 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 center oo z ulqu)3w35ig 0( pm3pji1c(qnl7kmf mass?

  16.50: A uniform stick of mass M and length L is fixed to rotate abou9/ni pdc8 .mrst 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 stick is horizontal, what is the tangential speed of the center of mass about the pivot? pc d.89/i mnrs

  06.24: A person tries to balan(fti0w kd o(+qce vertically each of three long uniform cylinders with equal radii on thew0iq tf( kod(+ 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 d -yx rlxw 7c13hes88fqisks,X 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 mounted to2b,kn*oi wkldqp0+;p rotate about an axis fixed through the center of th 2+qow;dknb*lk ip0,pe 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 disy8+gl0i jn7 0 ym2n+cw ljp5tsks, X and Y, have equal masses M but different radii such that tjiw+l g 0lcm njy7syn052+ 8p$r_x< r_y$. 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 ybqz a9-ov,;l cylinder with a mass M and radius R is pulled by a horizonvq;la9,y zo- btal force 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 disk5stsu1ccikj dv+.jgc: /,wj 5 of mass M and radius R rotates clockwise about its center w w.5,kjs c5 c/jv1+j:tdg iuscith 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 kg and radius:dsr+s-zbfmj0n*h q9 6se;z u R=10.0 cm is connected about an axis through the center of the cylinder to a horizontal spring with spznqrbm+ -j essh;df06u9 s *z:ring 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 engi/tv(u9xk 4w2;f aqf9 u+sz:rd* ywidsne 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 directiof w29/v+y sk;4uwuqdd*x9: rsizfa( tn as the pilot tries to make a sharp lefthand turn.