12.43: Several forces act on a rigid body. If the resultant (net) force6 rie10g x f7b*u7jpby on the body is zero, which one of the following statements 76u1gr0xi7pfejybb * must be true?

  97.39: A cylinder free to turnaround a fixed axipr87)m k+mlh rqu7uq3 s has a string wrapped around it as shown to the right. The string is pulled with a force rmk7)rh7u q u3l p8+qmF equal to the cylinders weight. What is the acceleration of the string?

  16.16: A uniform stick is fixed to rotate about an axis through its center. Th.jdkz 1exa2*ae stick starts from rest and rotates through an angl kaxej12 zad.*e 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 hjno,n2wy0uzaa ; 7*henergy K when rotating with constant angular velocity. When thnunhay2,0a;7j ozwh* e angular velocity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform spf3 7 sie)cjgpf07i t+mhere 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, radpex w9m8 an5,uabc411mbd b;nius 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 ank- y, hm (3w8cze3jjlrd an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of friction for the disk and ring with kh3yz-(rmjl,3 w8c ej 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 uniforkk 2mk1;gv* mrq3f:wo m ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of fricti;kk2go* v:mkqfmr1 3 won 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. Whic ahv q9 rx8h1ih0,xw ecfh1 i3u-ls)n2h one of the following choices best represents the type and direction of friction (if any) acting on the cylinder as it r )qirh19iuwlc v8s0eh 2xh fnx,a-3 h1olls up the incline?

  14.43: A long rod of length L is pivoted about its left end. Id fb (xn8ma26ht is released from an angle θabove the horizontal. (b2 dfhx8mna6 What is the magnitude of the angular acceleration of 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 about i9sq,3n 6 tjuua frictionless pivot located L/3 from one end. The rod is released from rest incrementally away from being perfectly vertical, results tn3u9ju ,qi6ing 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 t :ry 3ored3gzhkd4-q/ ju/0*rkbqr 0so rotate about a frictionless pivot located L/3 from one end. The stick is released from rest incrementally away from being perfectly vertibkq3 *erdzo0j 3ughsrd: q /r4/0- kyrcal, 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 three 2vlymmd; 0yu szv) 1-:dye6lalong uniform cylinders witvday1zy;md- ) 6se:m20 ulvylh equal 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, have masses ep io: jg+7yy-,pw1()mn ldda3 g brl9$m_x$<$m_y$, 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 unifo t9nwf2iz54dg c v0 1ws1gam5frm disks of equal mass each are mounted to rotate about an axis fixed through the center of the disk. Each disk is initially at rest. Thetf925iv ngc1d5 f0am wwg1 sz4 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 different r c.f 5s-wskkvdcq.4b8 adii such that5qf.k csc.b8s 4-wk vd $r_x< r_y$. 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 cylind,rpcahi t1n2h j ch(80er with a mass M and radius R is pulled by a horizont2 ha0 cj1(8t,h pchrnial 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 rotatesudp b42l0uw4w clockwise about its center b u04u4lw2wp dwith 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=103cya-p v wxj7 00vi+js.0 cm is connected about an axis through the center of the cylinder to a hys3x +v00wicvj j7 ap-orizontal 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 g3gvb8oqwjl.-g 6u .b engine plane are turning in a clock wise direction with respect to qogb..glw-g bj uv6 38the 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.