12.43: Several forces act on a rigid body. If the resultant (net) force 74ekfj;pe,)mhg a9oh17 azc uon the body is zero, which oeozuh ;hjfma74,7a ce1pg9 )kne of the following statements must be true?

  97.39: A cylinder free to tu:0fqet 1)lei83nuuttrnaround a fixed axis has a string wrapped around it as shown to the right. Thtu:1inquf8t eelt 30)e 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 axis through i)m l,a2r haax 95fb*zmts center. The stick starts from rest and rm ,z) mf r*a5haalxb92otates 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 fanl*dy;/* fo:wv/v q cn.z vd3h+e m:bxf blade has kinetic energy K when rotating with constant angular velocity. When the angular velocity is reduced to one-third, the kinetic energy bec x.v*;ezwf3q m :bc v/+d:vd/lnfoy*homes

  12.33: A solid, uniform sphere rolls without slipping on a floor alrcr p8rw1wb .z ,d9,ha5ew4t u2id. fsong 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, ra.(k1v-ubbldt6:, a)c i aj zutdius 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 an ideal uniform ring each dg2oyjlst( s* ps9k 7)have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of friction for the 2 ys s)s l7tk(o9d*pgjdisk 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 svbt-y b .v3vp*7 lag3x fx-zzjsxj*)5 olid disk and an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slippiyxatx5*vzbv* 3)bpfjvgx z7 ls-j 3 -.ng 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 rowk :iva *0x:vr5wv* ivugh inclined plane. Which one of the following choices best represents the type and dire: iw k*xrav5 v0wvvi:*ction of friction (if any) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of length L is pivoted about its left ed4m7ioew i +*n1hm8p+a:af h and. It is released from an angle θabove the horizontal. What is the magnitude of the angular acceleration of the7m++ph8wnm:hi4 od aa*a f1 ie rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M and f2e1 n cvu9cl.ka o6(hlength L is fixed to rotate about a frictionless pivot located La2vcc9h 1en6l.kuf o(/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 of mass M and length tsh-;d z(we yw) l9e:xL 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 ;d)szx -hew:ewt(l y9about 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 un/d,2ho:qw cr ei9f )qjiform cylinders with equal radii on thj hed9),co q2q/ :wfire 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 anl9g6d vd o+6/f s1zovndY, 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 massi4 iac/z1u 1xy each are mounted to rotate about an axis fixed through the center of the iua1yiz4 1c/x 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 Y, have equal masses M but different radii huy 3/b(dmk+ -ala+ti such th3-+ tm/ib+lhyauk(d a at $r_x< r_y$. 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 pe)kwnzn./j 7and radius R is pulled by a horizontal force F /jp nwne7z.)k 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 rotates clockw s; ku1sz ; gm vkjutz9dv3qj5y1(-wn*ise about its center with an angu* z 5;;j kzgwjkuq1svdu(m93 ys- 1vtnlar 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 ,tubls h(xywn6 x gq1wn,j0,+ of mass M=2.00 kg 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 springb 0lt,ghy( u1, 6j+,swwxnxnq 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 silu 4h 0z(jw5zqngle engine plane are turning in a clock wise direction with respect to the pilot. The gyroscopic action of the moving parts will cause the plane wj4 lz qz0(5huto move in which direction as the pilot tries to make a sharp lefthand turn.