12.43: Several forces act on a rigid body. tl4xugysx09, iue64v If the resultant (net) force on the body is zero, which one of the following ,xx 49 uuye tivgl046sstatements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapped aroun. zia4cnhh3vu+qs/ 4fctp4)f d it as shown to the right. The string is pulled with a force F equal to the v. h ft4fi43/ cquh)4nc+ apzscylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an ax1-cjnjouao3yb87 nt)8s1 pq tis through its center. The stick starts from y qt-a1on3bns 1)j78p utocj8rest 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 fan bladehk y,gnv 651tx has kinetic energy K when rotating with constant angular velocity. When the angular velocity is reduced to one-third, th6k 1x5h ,tygvne kinetic energy becomes

  12.33: A solid, uniform ;u np(08n vwbksphere rolls 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 inerfm -vgzm)ag3/ tia $0.5mr^{2}$ . 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 ha+mqfv-94 a.zx v;m9qtp6jmc/* pq rqsve mass M and radius R. Each object begins purely rolling without sc/av 9+m mx6vtpzq*-q ;r4. m9s fpqjqlipping 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 unifx8bm +nw cs rbag627d)orm ring each have mass M and radius R. Each object begins purely rg+c8as27bm b) xrnw6dolling 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 sl aob6 hrmi85o3ipping 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 up the incline? 3r5oh6obam8 i

  14.43: A long rod of length L is pivotbya4aak5v( wdcp6 3 9yed about its left end. It is released from an angle θabove the horizdk4b ya wava65( y93cpontal. 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 mass M and length L is fixed to orm:h/c,a;el m c4*ifrotate 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 acceleratimc ,ia;f/:em crlh4*oon of its center of mass?

  16.50: A uniform stick of ml9ds 3 2eqi4doass M and 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 horizontal, what iddo94 32eslqis the tangential speed of the center of mass about the pivot?

  06.24: A person tries to balbig;xwije)f 1+s )a4 uance vertically each of three long uniform cylinders with equal radii on the end o a+fb));eu4gi jx1iwsf 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, ha-k;devxhk 8ag) q 8jt*ve 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 rotate awtyp wtdo(j7 :u)y ; )kamfg8o7 s076 gmyswr,bout an axis fixed through the center of the disk. Each disk is initially at rest. The radii of the disktsj7 pmgrya )0o7, 6ymfw8sgtdou)(y 7wk :w;s 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, w2ez:-dfd cw;have equal masses M but different radii such thatf :wcz-d2;wed $r_x< r_y$. 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 wsaj+9kswda8 4hr *woi kum :).ith a mass M and radius R is pulled by a horizontal force F acting ua+ jkadsmo)k:49wr.wsi * 8h
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 radiusfx3gb *+* qcta R rotates clockwise about its center with an agx3cf*t*q+ bangular 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 conne ynp0lgq2kt.7o401q 4wx xe pycted 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 cente2w kx 040nqyqxl1te oypg7.4pr of the cylinder when it returns to equilibrium?

  01.39: Suppose the enrnqpw1 - 0ze hqcyd 7*bxz:8u+gine and propeller of a single engine plane are turning in a clock wise direction with respect to the pilot. The gyroscopic a-xr :enc8hy+q1up07dz q wb*zction of the moving parts will cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.