12.43: Several forces ac0 ty up1ig w.q4brahbg101.qe5jz3n r t on a rigid body. If the resultant (net) force on the body is zero, which one of the tbrng 1irep5w.u 30y0 zqgba1.j4h1qfollowing statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string pwq 2 +rsel5.awrapped around it as shown to the right. The string issq r. l+ewp25a pulled 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 ai9 rs54c1n;dk +kq gqup;,awf bout an axis through its center. The stick starts from rest q;k gr +s fn5dkc4u;wiaqp1 ,9and 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 rotatin9 6p jo1am84s4inhpd 2o;bmny g with constant angular velocity. When the angular velocity is reduced to one-third, tni4mo hm4p o8bsp6 219jyn d;ahe kinetic energy becomes

  12.33: A solid, uniform sphere rolls tg/dtznt;1l- 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, radi y 7( h1x1m21(eksrhatfv4kxa us 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 soli2yv; p57vk7g- zzrrr kd disk 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 and ring with the gyv-7r72zz5k ;pkvr r 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 unifopz -bi gvi,g7fdgau 5zf w0 ,9rgy+-+trm ring each have mass M and radius R. Each object begvf +7fu,ytiw zg0da+ zg -9r5b g-,igpins 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 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+5dk/(1qm 4 3)ic1pej g 6fpnww litee rough inclined plane. Which one of the following choices best represents the type and direction of fri+wki( qctj p iwdn/e516)4gle1femp3 ction (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. It is releasedotr/7*9d c(nqi o*fbt )psxct96x*cc from an angle θabove the horizontqsr( t697co f*)t x*db*txi 9 /pncccoal. What is the magnitude of the angular acceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod of massc + pjhqt07*be(g 9qyt M and length L is fixed to rotate about a frictionless pivot lc*7j+byg0 t(t9qh qpe ocated 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 mass?

  16.50: A uniform stick of mass M and leng9ic ,:demjm/b th 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 mbj ,9cm:ie/dclockwise 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 each of three long uniform cylindersnj aed4 tkm4rz)54 a9n with equal trma njn594 d44a )ezkradii 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, have mass: 7n4nsqkymvzf- 6 ie)es $m_x$<$m_y$, 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 equal1b3t9 hybv. 5jmmbbzk(/qy o , mass each are mounted to rotate about an axis fixed through the center of the disk. Each disk is initially at restz 1qb.,v3 b(tj /mbmo5byhyk9 . 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 disk i5*--gpykuplvoz 2j 3s, X and Y, have equal masses M but different radii such tha 5pg upk-i-*2lj ovzy3t $r_x< r_y$. 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 x/96b,oohwzb is pulled by a horizhow ,zbo96x/bontal 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 ab i-h u+g,d,(kvijz9zxout its center wit+-,g kd jzv9hz,(i xiuh 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 cylinde hiqsutk 84,c09z60u;;lypaqi aq,wxr 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, stretching the spring 1.00 m from equilibrium. When released, the cylinder rolls without slipping. What is the aq84hi 0s,6kc 90z luqap;tq;,xuw iyspeed of the center of the cylinder when it returns to equilibrium?

  01.39: Suppose the engine and propeller of a single engine plane are turn g,3hjgj tvy:.ing in a v:, 3 g.jytgjhclock 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 make a sharp lefthand turn.