12.43: Several forces act on a rigid body. If the resultant (net) fwh+5czj ; q9 yjwfg,0sorce on the bos fg 9 y;j0+5cqw,whjzdy is zero, which one of the following statements must be true?

  97.39: A cylinder free to turnarou7 g5+ ;kujhvlpnd a fixed axis has a string wrapped around it as shown to the right. The string is pulled with a f jh +lv7k;pu5gorce 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 center. The3jetpn0r bz .+y e9p9 pgh,ss7 stick star s0g 9b,e3.h+nryst79z jepppts 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 energy K when rotating wittbs zv-1pod-g (v elu ve-nf*+df5q8.h constant angular velocity. When the angular velocity is reduced to one-third, the kinetic energy*-1g+dqzv- fo pnv8el tsfd e.(bu5v- becomes

  12.33: A solid, uniform sphere rolls without slipping on a flooxpkfsue- mmw37 /2fx 0r 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, radt:zd1 z5-sgf( 2l-jriavb4 x kius 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 each+l 2if5cgamsdcx ky 83 59:vcm 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 ar y55:9ldmf+38sx2acmvck g cie $μ_disk> μ_ring$.
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 unifoc2arz5;hw li(3 s+ it q9:qk e l)vas-jl7f0vdrm ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough incl:e20)s wi+lqdcvr-hqj z;l3asl5 (9t k vif7ained 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 inc;zc 9tec3kv3 dlined plane. Which one of the followingt 3zck3ec9dv ; 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 +telfemji90, its left end. It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about tm0lfi9 t,j+eehe pivot when the rod is released?

  15.46: A uniform rod of mass M and length L is fixed to rotate about a :ktr1g /k ,zadfrictionless 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 of mak/rd1ga, :zt kss?

  16.50: A uniform stick of mass M and qzg43,adnjy6length 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 perfectlqndz6ay, 43gj y 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 balance verh. -2.i kxkb5mr l7scxtically each of three long uniform cylinders with equal radii on the enl.k r7mchxkxs5-b 2 .id 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 g;bkp ig(ly2wku z1x. 8b ybw, uqft;/zt-*o8andY, 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 uniforw ( dl8-oj)g4ypem:mbm disks of equal mass each are mounted to rotate about an axis fix:m eomb4j8wl()g- py ded 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 different +n hhfbbj4 0d7q:gc0xradii such b400+qh nc fdx7jhgb: that $r_x< r_y$. 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 hor/*4r ih1 dy fgj/j4euvizo4 v/1hy/ugd4 fejir*jntal 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 disk of mass M and radius R rotates clockwise abo( :tcg-mo;e zqut its center wi tc- mzo(:gqe;th 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 R=1:/je ,kn r+mzs0.0 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 pul/z:n+ser,jk mled 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 jv5ahm74jg nuhe m*w s9u+ -4*bxk .gqengine plane are turning in a clock wise direction with respeq9-7m *5ubwxe*g4 sm.ghv uhjkan4j +ct 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.