12.43: Several forcegl4tq 6* fh8l 0 lv6 jgcq9v22vrf7rx7jge+yz s act on a rigid body. If the resultant (net) force on the body is zero, whr j+jgy04lg qf7gq tvh*frv689vl l6e2c7 z2 xich one of the following statements must be true?

  97.39: A cylinder free toi1vyb ej,l i0nf0 d ;yodz3x(3 turnaround a fixed axis has a string wrapped around it as shown to the right. The string is pulled with a force F equal to the cylinders weight. What is the acceleration of the st dij,dnl 3;yxi31 ( yov0fz0ebring?

  16.16: A uniform stick is fixed to rotate about as2;k)xduxr rux.77ezjf0 ;-3 qmzcw mn axis through its center. The s)7 ufxzezmr;uw7c x qjmr0xk;23.d- stick 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 has kinetic energy K when.y p*uabrb6my d1;- bf rotating with constant angular velocity. When the angular velocity is reduced to one-third, the kinetic energymrybb6-*y 1;fpub a.d becomes

  12.33: A solid, uniform sphere rolls wit 2jt9n. ordu-r-) (5hfapo01 g*byfi4gszs m zhout 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 inertus6n xz i:gb9b-oa +u)h:ewb,ia $0.5mr^{2}$ . 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 mass M fjcw3l*d 8q 2jbt hsw+iq4: u2and radius R. Each object begins purely rolling without slipping down a rough inclined plaj+ h4w2c*3s u:t j2df8qwb lqine. 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 uniform ring :zotnvk2j b):pp1)xr3wevbrsg6: w + each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plan r6e o+w: w)ntp3p2kgb:j:bz)vx s1vre. 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 slipp g7/;jrgv6le7dgoealk - wh(80(pr vwing on a rough inclined plane. Which one of the following choices best represents the type and direction wpa776j ev08(kew/l -go g;vg hldr (rof friction (if any) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of length L is pivoted (z3j0/c8 sezjw/ao 1ype)yl r about its left end. It is released from an angle θabove the horizontal. What is the magnitude of the angue0 (p1o)jwz3ze/yy j/c sl8ra lar acceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod of mo0a8sqjn*yjng5e +x i,p37v qass 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 t+s7*8 vn0in3qj ,joqgxpae5yhe magnitude of the tangential acceleration of its center of mass?

  16.50: A uniform stickum7ug l a 0fva2oo83p; of mass 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, resulting87p3fu u;o2olag0am v 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 ubuc) n+gl/- cvniform cylinders with equal radii on the end of his flv/nucb -+)cg inger:
• 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, have85 wuh8cs8ab hed qo(- 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 mount+v n*7m,(qvad.ccojp ed to rotate about an axis fixed through the center of the disk. Each disk is initially at rest. The radii j*p7(o,q .v+ dvnccmaof 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 dy9,da- lppx6uisks, X and Y, have equal masses M but different radii such tha9 ud6py-,alx pt $r_x< r_y$. 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;dv1x s9:hti by a horizontal force F actingd ;ohiv1s:9 tx
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 cloc-,b9 jko3 a l2pdzium1usgb -/kwise about its center with an azuj-g,9 d3 1smkuib a2-b/lpo ngular 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 ebp0c-9:epg zkg 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 slipping. What is the speed of the centceepz9g p-0b: er of the cylinder when it returns to equilibrium?

  01.39: Suppose the engine an9ca40.y 7 7gzzlp,kuoj 7nglj d propeller of a single engine plane are turning in a clock wise oy,4p7l j0a zuclnk g.jg7z79direction 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.