12.43: Several forces act on a rigid body. If the re2j zkzp4pt 48xjt -jd-sultant (net) force on the body is zero, which t8jdp kxt 4-zjj- pz42one of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has azr+:4zd9hdim(5-ayvd s0 jvw string wrapped around it as shown to the right. The string is pulled with av-9 sd0dw rv4yd zhaj+i(z5:m force F equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate w4o.wgb(:rc kabout an axis through its center. The stick starts from rest and rotates:g(c.rkw4 ob w 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 rotatin:kr z+l.r30/h twiuk jg with constant angular velocity. When the angular velocity is reduced to one-third, the kinwrt+kh r3ukji0 l:/.zetic energy becomes

  12.33: A solid, uniform sp; jptq wvgu 4(s8k1/sahere 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 rotaa-uh yd4r h-qcni1fsh/6l,b9vpb-(ktional 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 idea b8;3ckjm qeb.l uniform ring each have mass M and radius R. Each object begins purely rollinbq .mk3e8; bjcg 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 and. *h 2l3+xwz3z apkoi4x1omk ideal uniform ring each have mass M and radius R. Each object begins purely ro4 +zmhxzkk p* o3d1ixw3o2 .allling 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 r4x/0 r8ypa w g6,xkwnvough inclined plane. Which one of the following choices b/8x ar4wp6 ,ykxg0vwn est represents 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 pivos gl cv;vw8-j r,nu-)dhci* +fted about its left end. It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the rod about the pivot when the rod is released? ln-sv;,c v8- crwiu dhgj*)+ f

  15.46: A uniform rod of mass M and length L is fixedjew fbm 4xx / *ip0zpyx2a0x-5 to rotate about a frictionless pivot located L/3 from one end. The rod xmi2fjy xxe* z45ax0w-/ p0b pis 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 length L is fixed to rotate about a fricti/ k)zght8v6j3 (d0cgn t8qqnjonless pivot located L/3 from one end. The stick is80q6z)cknj(v j dgn8qgt /3 th released 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 th+i2 y72lb1j;/mkadq6n va+d zd eq:faree long uniform cylinders with equal radii on thla 2+7mafz/ekqjd 2n1idq 6d;ya + v:be 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 aa :ryqd mns,d:lv:7 4,gjn4qyndY, 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 di: w 1nxmo 1;yen zj(9(u1ila5oqqqcc. sks of equal mass each are mounted to rotate about an axis fixed through the center of the disk. Each disk is initially at rest.n1cz (q.qow 95x( oa1:uyj;l1 m cqine 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 mavd/642 wxb prj z,af2hsses M but different radii such tw 2/p6,4j2a xzdb fvhrhat $r_x< r_y$. 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,:j x ;aihx+fp radius R is pulled by a horizontal force F acting +jif xp,:axh;
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 8qwms21 u9 i+er :ri ebpo 3-y-1rdxuwdisk of mass M and radius R rotates clockwise about its center with an angular :ber1r3y +9 r8xwie-q ups2mw- d1 iouspeed $ω_0$ . 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 co* lrtovij57 37vwux;hnnected 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 wiuivorj5lv th7x;7 3w*thout slipping. What is the speed of the center of the cylinder when it returns to equilibrium?

  01.39: Suppose the en. a -w kve(1h;wvm)8ei9un.wjqhpc 5y(a bq; ngine and propeller of a single engine plane are turning in a clock wise )i85njba hwww-(q;1u qne ( hmvpv..eka ;9yc 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.