12.43: Several forces act on a rigid body. Ib5n:fy.9 v0ljre ua /af the resultant (net) force on the body is zero, which one of the following statements mujna r/e0bu 9ay:flv.5 st be true?

  97.39: A cylinder free to turnaround a fixedj6i):s/h8glq( *t/yeehjg p s axis has a string wrapped around it as shown to the right. The string is pulled with a forcese htl8):6iqhy/jg (*pesj/ g F equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis thro p 8 qq1;3*fp gyg+u1uhf5bswo0s,k 6r)a xhmcugh its center. The stick starts from rest and rotates t)u1 s5uyfgphxqf138a6ks +pch,gmq ;*b row0 hrough 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 gr6ymh/ rb4(t mi03 ,/yzgkdn kinetic energy K when rotating with constant angular velocity. When the angular velr0ti h(kgyn4//,dg3m z ry6m bocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on a floor along,z.f1cf di dn nk*h26/jrovh: 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 masbumq( .q 7dqe4s m, radius 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 solid disk and an ideal uniform ring each have masa (ycwf -.2efgs M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of friction for the 2a.-wfegfcy ( 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 an-88: jdx cnaicuwe,m1 d an ideal uniform ring each have mass M and radius R. Each obje :1m8c-uadn ixec,j8w ct begins 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 rollsa8 q y0 k:lukxkeroqxq3p51 17 without slipping 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?koqxl850:q1 xq ru ek71y kap3

  14.43: A long rod of length L is pivoted about its left end. Itzdn*y +eyo2rcq/: .fm is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration ofd r z*2y myo:qf+c/.ne the rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M and length L is fixed to rotate abk xm4-ka *q 5g3t+tfhrout 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 acceleration +-qktr 4ag* 5fthm3xk of its center of mass?

  16.50: A uniform stick of mass M and length L is fixed to rotate about a lpwemo7mg m m+lqnb2.f( p2-,frictionless pivot located L/3 from one end. The stick is released from rest incrementally away from being perfectly vertical, result2w,2 +emb.-(omm glpnm fq7l ping 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 long ubrt c.9djq kadm6/2u2 niform cylinders with 6j /2m u9qdta.2ckb rdequal radii 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)ki 6in ,t7wh0(jxrmh, 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 .u7p,wv7ij pq equal mass each are mounted to rotate about an axis fixed through the center of the disk. Each disk is initially at rest. The radii of, 7v.qjpw7 upi 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 diffekk6 w*f)wzm ,nrent radii such that)*km,wwz kfn6 $r_x< r_y$. 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+ j(d6igr0v/mlq/m y e a horizontal forcige/( dqjml v6 0my+/re 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 e0( f -g5e(gzfxn fyx6wsjz )e--c1ptclockwise about its center with an angular speed g 0js56ntxw fe)-xpec-gz 1 (e(zfy-f $ω_0$ . 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 r r:n ejqq-v*kpkt+4,mass M=2.00 kg and radius R=10.0 cm is connected about an axis through tht kq k,v :+nep*4jrq-re 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 center of the cylinder when it returns to equilibrium?

  01.39: Suppose the engine and propeller of a single engine plan0joyqmyq( (k,e are turning in a clock wise direction with respect to the pilot. The gyroscopic action of the moving parts will cause the plane (o0 ,qjyykm (qto move in which direction as the pilot tries to make a sharp lefthand turn.