12.43: Several forces act on a (up41peipxi)f x.i4p rigid body. If the resultant (net) force on the body is 4pp)eu4i(p1. ip fxi xzero, which one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapped arou.af9vz6b gy a8nxh)s5z .m9gknd it as shown to the righfg .8aagxhvb5.9kyns6) m 9zzt. The string is 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 about an j-.gq u) ojc3maxis through its center. The st ogq jmcu.j)-3ick starts 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 fanliaeac9; +u3jbmzo:w me 75.w blade has kinetic energy K when rotating with constant angular velocity9.jz3 o5b cile a: wam7e;mw+u. When the angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor along the jqs9 jo z1i/w*.bx/ uspa/ n2b$+x-axis$ (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 rotm.tntj0 3qj3national 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 so yl.a./ 6bsg bvhj-ia3lid disk and an ideal uniform ring each have mass M and radius R. Each object begins purely robi3aa.6lb/g hy-. vjs lling 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 an ideal uniform rin5 br,ko zs2qmcu-dj07g each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined placb,j 5s 2qo7ud0mkrz -ne. 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 sli ntia(ni+()9* yln eezpping on a rough inclined plane. Which one of the following choices best represents the type and direction of friction (if any) acting on the cylinder as it rolls u((*+ ltneai zi9ne)ny p the incline?

  14.43: A long rod of length L is pivoted about its l*)qo.cqbmtn 2 +md-rieft end. It is released from an angle θabove the horizontal. What is the magnitude of the q-c)tq+n r* mb.dim2o angular acceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M and le 6j5kcz z,ci9bngth L is fixed to rotate about a frictionless pivot located L/3 from one end. The rod is released from rest incrementally c j9,i5 c6zbkzaway 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 length L is fixed to rotate about a fr5. qfr wbs/ y2,1fzgxdictionless pivot located L/3 from one end. The stick is released from rest incrementally away from being perfectly vertical, resulting in the stick rotat xwr/z.,f gfy5d1sq b2ing 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 vertically each of three long uniform cylin4e2 6,cdrd ; a,g(: rbheg.r7-pfphayh l.jfaders with equal radii on the end of hrdfalh 76c ,phhab 2y g4-er p(fd:e gj;,..rais 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 dis-;fys)fryl x+ ks,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 tow ngcaar *7r ;62y 0foaaeb9lit8-/ ze rotate about an axis fixed through the center of the disk. Each disk is initiaaaang*z yi 2wcoft;8l6b 9 /7-r0aerelly 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 radii st4 ki.s9w id,fuch that .fd94 ktii w,s$r_x< r_y$. 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 cylinde igo/6mq5u1pn td2l 7rr with a mass M and radius R is pulled by a horizontal forcgol/t7iud5q6 p21 m rne 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-prcitnq-cest:3 1 z- and radius R rotates clockwise about its center wiz-ri- t:- pnc3 q1scetth 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 b(gj 2fu0p,2dh znuz5 kg and radius R=10.0 cm is connected about an axis through the centerpz(u g2f0dh j52n uzb, 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 equilibrium?

  01.39: Suppose the engine and propeller of a single engine plane are turning inc ivm .1gozv9r8-i6w q a clock wise direction with respect to the pilot. The gyroscopic action of the moving parts will cause the plane to move in which d -vrgqozi6 wimv 9c18.irection as the pilot tries to make a sharp lefthand turn.