12.43: Several forces act on a rigi an30xij 90njqd body. If the resultant (net) force on the body is zero, whichq n3jainx9j 00 one of the following statements must be true?

  97.39: A cylinder fre67xuaeeuv(esk1 g f,9e to turnaround a fixed axis has a string wrapped around it as shown to the right. The string is pulled with a force F equal tee(uku, 91v6s gex7fa o 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.ic, 67yfdkkv +vvt e5;i)bq4g The stick starts from rest and rotatkq 5 +6vi7gdc;) vty 4fvk,ebies 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 h88 brtntwt,k*as kinetic energy K when rotating with constant angular velocity. When the angular velocity is redut*rttn,8 b8wk ced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slippi (bjjeyz .z+ 4w d1fehf0su4h*ng 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 inehba2fm+ z;d+ m8 wki;xrtia $0.5mr^{2}$ . 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 have mas+uzbf)5g 4 a)jeze* qfs 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 w)u)zeq4*j gaz+f 5ef bith 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 t, 8p*sq3(o5uiphdkjring 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 diskp,p* tk ousidhq(j 835 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 spuda8-32v9 jgjcu x6j lipping on a rough inclined plane. Which one of the following choices best repx- dpauj g62jjv c9u38resents 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. It i4 v,p6kmn0lo,re yo(rs released from an angle θabove the horizontal. What is the magnitude of the angular po0,rer,lm6y k4vn o( acceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M and length L is fixedxo,u rapy+y c8p37 *pi 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 horizontal, what is the magnitude of the tangential accelex pcrp 8oi3y*+u7,ap yration of its center of mass?

  16.50: A uniform stick of mass M and length L is fixed to hg(z2zktu 1vso g,( 3arotate about a frictionless pivot located L/3 from one end. The stick is gaz(ou 1ts,hgz kv 2(3released from rest incrementally away from being perfectly 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 vertically each of three longur1 ;sdy zr4et9u39j d uniform cylinders with equal rj9du rr zu3d4e;1ys9tadii 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 an.;a.pe-te:pc f*1ur rghs6s wdY, 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 to rota*p pwa+(xl b(lte about an axis fixed through the center of the disk. Each disk is initially at+ba* l(x(pplw 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, h/0as9 6flrd hz :.t ad4h yqw-00feuqqave equal masses M but different radii such th: td4q6lq0w9dqry.f 0ueh azsf h0/a-at $r_x< r_y$. 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 radiul-hhs s856asif nr;5w s R is pulled by a horizontal force F acr;58ws5sf-nai hs l 6hting
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 3jxfv6 g0n 0)wy xa9mlabout its center with an vj9xmn0x) gw3al y f06angular 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.n ,discbe4ur,k8se(:e/+ ydh00 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 sly, /8eheiedn, (4d cs+ rukb:sipping. 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 en wsdb2ka8kcp- gp,o;,gine plane are turning in a clock wise direction with respect to the c oak,pdkp2;wgbs8,- 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.