12.43: Several forces act on a rigidp+v14vc*d wzwyc il *: body. If the resultant (net) force on the body is zero, which one of thei y:vp wc+*lc zd41vw* following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a strs7y*v9k 81dwq.yuh v iing wrapped around it as shown to the right. The string is pulled with a force F equal to the cylinders weight. W*8duysk 9vyqvw hi71.hat is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis thrrd6caf 3r v-hgy1z*si3bd/+ bough its center. The stick starts from rest and ro zhr3*id1s f by- r/vcdagb+36tates 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 energy6 xz)fsokjj8q 6mc6*b+v fe bt k9iu,- K when rotating with constant angular velocitb f)8j6,bvkq sj6* cm zto fei9-ku6x+y. When the angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls wi4 b9y3gnpew,,x(n fkdthout 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 r, and rotational tk7-zq- eo (hwok s4n;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*guol-5i drj9 and an ideal uniform ring each have mass M and radius R. Each objec*l d5rg9 oj-uit 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 ann4eu+w 1r 2bdzp+ dk;r 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 incline andk redu4 w1+ 2bp;+zrre $μ_disk> μ_ring$.
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 inclinednp*y4ob9 s /d um7pdv;a-2k dc plane. Which one of t9yvk -*/ ;2ca7udnp4spo db dmhe following 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 end. I6zq, 0wzjw80n . qlk3qsu:yj7xdbr 8e t is released from an angle θabove the horizontal. What is the ma3rejq d, zx nu7b0qz8ww0:kls68j y.q gnitude of the angular acceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod of myw7is6)eef/wc )z l .t+l/zdht *ns: wass M and length 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 perfc +/e.flw/nyzswze6:d hl stwt7 i)) *ectly 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 mass?

  16.50: A uniform stick of mass M e+ j;/d( gthykand 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 perfectly vertical, resulting in the stick rotating clockwise about its pivot. When the stick is hori+(/ hgktj d;yezontal, 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 )zc ilbodl1)w i5s6+ hr4vy ;funiform cylinders with equal radii onb zy 4v)icod+lih;5f r 6)wls1 the 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, have masses uiv2)7ic3i y k$m_x$<$m_y$, 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 rotq1w9it j8d y l,yue5y8ate about an axis fixed through the center of the disk. Each disk is initially at rest. The radii of tl 98y,5ey1ju dqi8t ywhe 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, ha/z rrw66 (purfve equal masses M but different radii such that f(6wru zr 6/pr$r_x< r_y$. 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 withuss.)+e jkym6 a mass M and radius R is pulled by a horizontal fmk. +jes)us6yorce 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 phz, kn xe 7x0,hf *pq8qd29rvrotates clockwise about its center with an a p7*xp0fv8k2h e,qxd, z qhn9rngular 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=10.0 cm is conneq+ nycy1xdvf2ta*a-e3js;e;d9 tgj , cted 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 speed of the center of the cylinder when it returns to equilibriu jj2 tv;ada g,*xn9tsy1 q+dfe-;yec 3m?

  01.39: Suppose the engine and propeller of a single engine plane are turning c7 8/is7au ulrin a clock 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 make77s urlauic /8 a sharp lefthand turn.