12.43: Several forces ah + w*ejw 4mwo+ozas vz6gcpyo+4:-;bct on a rigid body. If the resultant (net) force on the body is zow-ha6+sb+o g :ep c;w4zmv j4o +yzw*ero, which one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has+ vmeipcd6d3em u, r24 a string wrapped around it as shown to the right. The string is pulled with a force F equal toeumcd3p+e 6d2,iv rm 4 the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed ; csg418bu c+ 1chyj1yd1gx wlto rotate about an axis through its center. The stick starts from rest and rotates through an angle of lcc4u1x8ydg;cby+ whsj g111 $90^{\circ}$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 rotatingvb6oz a7pjr29 a su50f with constant angular velocity. When the angular velocity ispbr5 6us7zfa9 a0jo2 v reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rov:p( v.eftjz-o iur88lls without 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 inertia f7/9rgl-bfha+qe/o5u eg .th $0.5mr^{2}$ . 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 unitcj33w psi ,) 5ihtmd0)31ghvcf k1plform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of frictiopc1t33w)mi,dl0 p tc hf)35 vg hji1skn 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 uniform ring each have mass8z/y5ju9xr * g8pi*obrmh-qh 3x( jfv M and radius R. Each object begins purely rolliyvxrm*8hpbo83/( r 9zhx 5g*qu-ij fjng 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 withoutuvqm .ozn5.otby c *rm e3mi5/dk962z slipping on a rough inclined plane. Which one of the following choices best represents the type and dire* 26yizn5ocuktv d./ozmmb3qr.m5 9 ection 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 ioi-g d9 d0 fib:2ne*xjts left end. It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pivot when th9 xd 0:noigibejd*-2fe rod is released?

  15.46: A uniform rod of mass M and length L is fijfkxka50 cme/(jw d3 +xed 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 +50aj3xc/mkj d fe kw(horizontal, what is the magnitude of the tangential acceleration of its center of mass?

  16.50: A uniform stick of mass M and length L is fixed to rotate aboto4/fql1f95f e m.ptk ut a frictionless pivot located L/3 from one end. The stick is released from rest incrementally away from being perfectly vertical, res19tfq 4fmk. t5ef lop/ulting 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 vern +e1 6o+shmiltically each of three long uniform cylinders with equal radin6me1 hl +i+osi on 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, hbx*i2hhj-9mase x (a0ave 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 0n o.m:e1ia6vu ,sszrare mounted to rotate about an axis fixed through the cente zru m0:6o,1svnis e.ar 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, 2hrst4b: q4z/;it:myceq nv Y, have equal masses M but different radii such teym z,qth : q4cis/;4vbt 2:rnhat $r_x< r_y$. 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 +79v7fbtyakihorizontal force F actin7a y+9ftv kbi7g
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, uniform2ci:v8 1geursuv5r)r 9;kmfv disk of mass M and radius R rotates clockwise about its s veru1 gr;82)ciu:vfv m59rkcenter with 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=10.0jaffn p8n9hzb.2jv . 2cvz4gnz:a1a 1 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, stretching the spring 1.00 m from equilibrium. When released, the cylinder rolls withoz2 fzn.h119zfjn. a82 gpvvncaja:b4ut 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 planesqlingrmw,t0:x tq 9f-a7l-) are turning in a clock wise direction with re-tr-x )istmg 9q fla:7l, wq0nspect 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.