12.43: Several forces act on a rigid body. If the resultant (net) force o lryx2 ize7*w7qoo93cn the body is zero, which one e2qzw3oy 79i*clo7 rx of the following statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a string wrapaev ,kmy(mvz) f06-gmped around it as shown t, va)yez6vm0gmmk- (f o the right. 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 9x)6h ljs - ced5yltibsfx ;3)rotate about an axis through its center. The scxfblj6 ey5 )9dh3i; )l ts-xstick 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 fan blade ha4pl) h6b 9i0n.jjdrrj s kinetic energy K when rotating with constant angular velocity. When thelj 6bhrr 9.4jjnp) 0di angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls withoup- ny il.pv *o:n(*k4v/lp sdbt 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 x 09xb+ry0wp brotational 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 hap) v.b (ktd :ko5u.az;mofe3mve mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of(m5ka;okpfz3 .)t vb mou .de: 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 an1:e2r wj.hmah ideal uniform ring each have mass M and radius R. Each object begins purely rolling without sh2:j1rw .he amlipping 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 sli1 dg1krxg1ix ;pping on a rough inclined plane. Which one of the following choices best rxgirdx 111 ;kgepresents 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 5 44k t18qm yzkif8bqlpivoted about its left end. It is released from an angle θabove the horizontal. What is the magnib8q lt k 8q4kfy5m14zitude of the angular acceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod or(e*2mpfo4w h hbtq .)f mass M and length L is fixed 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 acceleration of its center of mass? em*ow h2) bhfpt rq.(4

  16.50: A uniform stick of mass M and leng ,. clt90adp7yi.g aygth 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 is the tangential speedtid 9g0.ay pl cg,ay.7 of the center of mass about the pivot?

  06.24: A person tries to balance ver w ;/qmphudx9o:6o5 a zbx81mttically each of three long uniform cylinders with equal radii on txxwm1dqtbu6 z9o; :o/hp8 a5m he 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 disis x -emaz.28rks,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 mouj2/3,+3j op xeasb.xkmtz i0b g5nii iws8+,f nted to rotate about an axis fixed through the center of the disk. Ea8a0, +bs+,fk/ii5pej.io jxnxw23 ibmztg3sch disk is initially 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 dif a9, 9c2*xa1lkh(fp smpt2j buferent radii such thah 9m us*pjkp2 ab9( fx1t2c,alt $r_x< r_y$. 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 pulledo,xw(gxl kkdjaw3j0x7 h735v by a horizontal fora0xxgd5,k77l3 v (hkw ojj3w xce 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 radiu17icp 8arh,ol s R rotates clockwise about its centr p7 81cialh,oer with 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 kg and radius R=10.0 cm is conn(1d: s (ob2l qlatgt2fected about an axis through the centesfdgltqb2 l2 1a(:o t(r 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 m,-ajg-blc5 ;o:ovs cpropeller of a single engine plane are turning in a clock wise direction with respect to the pilo: 5vs ;al,jobmc- go-ct. 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.