12.43: Several forces aczl2t;rq+6ivehd- hf8t on a rigid body. If the resultant (net) force on the body is zero, which one of the following sta+ l2hqzehvr t6di-f;8tements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a-6 ,j ldjys( oot;bfu- string wrapped around it as shownstjou;l(f--b jo6 dy, to 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 rotate about an cm5c8ik 6rxx4 axis through its center. The stick stxkm86x 5cr4 icarts 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 wheg*nr+vj) 3oe m 8jtak*n rotating with constant angular velocity. When the angular velocity is reduced to one-thi*8g*ne3tjm)korv+a j rd, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without adlf1di y wijtj6*3.3 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 )8x nvy)xchm9q-ha +h5giz -x 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 :e- 4hx kkj x(x8unqct,hxem9d8w1 x,r,ezg -an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping dzmxh(udhx ,kg:8r c -xk91 exnq 8jx4teew,-,own 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 uniform ring each*z8ych* j r9dx5./(xz r 4ae mnm9ehgg have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. g4ex9.m9x j 5z(8r*h/rge a z*dych nm 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 rough inclined plane. pckim9 3f/pgh 5rvg 23Which one of the following choices best represents the type and direction of friction (if any) acting on the cylinder as it rolls up the inclivkr35 pi ghg9/ c3fm2pne?

  14.43: A long rod of length L is pivoted about itiov.q 9 w. nmda+3pop2s 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 reom+npwa .3. o ip9vd2qleased?

  15.46: A uniform rod of mass M and length L is fixed to rotate (5 v)+* 2jmr* htwnq bnoc6lvsabout a frictionlesbl2wo*t6 nscrn(+j )v*h qm5 vs 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?

  16.50: A uniform stick v6obsldj9yy*y s9 g; 8of mass M and length L is fixed to rotate about a frictionless pivot located L/3 from one end. The stick y y;l8vsosy9 9d*j 6gbis 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 verti blj+gpv49zf8 cally each of three long uniform cylinders with equal radii on tvgz9 p4lbj +8fhe 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 )3bhemo0 swz-gha9: m 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 mounted to rotate abouxl(5gfq+astdp3 b t:mg3) c8xt an axis fixesgf q xtda:tc b+ g835l)p3xm(d through the center of the disk. Each 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 ps0ldeuqw,. 0 Y, have equal masses M but different radii such thael, s00qu .pwdt $r_x< r_y$. 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 radius0i. ,cdkrlm8zbuapm :w f+ b2* R is pulled by a horizontalw bkcb:,mumdai 0p*l8fz +r. 2 force 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 rotant3q 7uew 7ih0m;) o3nkk htj5tes clockwise about its center with uqhhne5t07t7)3j kown mk 3;ian 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 radiusk ln0rm3a4r p 0vo,*df 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 center of the cylid vlofrprn *0, kma034nder when it returns to equilibrium?

  01.39: Suppose the engine and propeller of a single engine plane a7u 6 bn*,pejlare turning in a clock wise 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 m6p*jea7ul bn ,ake a sharp lefthand turn.