12.43: Several forces act on a rigid body. If the resultant (net) f.o8rgbi. dy1h orce on the body is zero, which one of the fo.r yi.hdb 8g1ollowing statements must be true?

  97.39: A cylinder free to 5jy;ohh /)jnf,p4vny z yc 6*bamw11v 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 mzn v yw/pchjjyoh1 5b,)61 *vfy;n a4of the string?

  16.16: A uniform stick is fixed to rotate about a+3 w*e zmo;sgnn axis through its center. The s ezwo;m+n g3*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 whe1 jhpd*s-5rttn rotating with constant angular velocity. When the angular velocity is reduced to one-third, the kinetic ene1tj5 td rs-*phrgy becomes

  12.33: A solid, uniform sphere rolls without slippingamla0n c +s 8yc)0p,pg 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, rau9 /ivdmcd6y5 dius 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 an5:v;p*sm psrr6c la(x ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The( *6pspc:rx; 5rslavm 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 jm419yel:sb- ea,-bzz ldj k d.0nxl+disk and an ideal uniform ring each have mass M and radius R. Each object begins purely rolling without slipping ajnl0- .zksyl4mdz,+d jlebe- :1x 9bdown 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 onhv:-ze5 g1l fr-ewz e)m0+b mg a rough inclined plane. Which one of the following choices best represents the type and de+-v z1r ge mml:)egzbw-h05f irection of friction (if any) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of lengtcs63ck4nfx7,ptu7 a nh L is pivoted about its left end. It is released from an angle θabove thsccf a3n,t6u47 7xkpn e horizontal. 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 rotlbqd8 5u5t222/ b xl qeb(ysayate 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, wh 2aqtq 2b/8l5 b5lu yxde(bys2at 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 to rotate ani5*vh iy y0.0gj, bvkx)0dks bout a frictionless pivot located L/3 from one end. The stick is released from rest in, gkvdn y00. *sk)ibj 5y0xhivcrementally 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 vertically each of three long unifmym gr26 nsiiq,hwh-s;f.:2oorm cylinders with equal radii on the eng2 hw.yif sm 2;:-nosmih,6q rd 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,t. .)uq)ul .9avgqdcg 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 mountedr-xm)c gklrtg53hhg0 viy6 jnem .6iq1t.l :7 to rotate about an axis fixed through the center of the disk. Each disk is initially at reiv- iyx.qjr6l )cmmth 3765ggehntg1:. r 0klst. 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, hav z.t9df6nk)ofx6tx 26 cy gt)ie equal masses M but different radii such tft6 z6y6 x kttcn)i.fogdx)29hat $r_x< r_y$. 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 (s t30 eq+itbnu*u,kx u92-zpe8z xij radius R is pulled by a horizontal fo +*tk(zex0,x 93 utsunue-8j biqipz2rce 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 rotates clvc)30rqj k 0wk2fo 5nuockwise about its center with an angular speeq0)v kwn c2o3fk0r u5jd $ω_0$ . 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 solivsl( 7;-f 8 mqajpuxq(d cylinder of mass M=2.00 kg and radius R=10.0 cm is connectedqfm8v(p;7uql- sx( ja 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 cylinder when it returns to equilibrium?

  01.39: Suppose the engine and propeller of aefy1p96 l6u ml8ay n6dw,o.hp single 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 to move in which direction as the pilot tries to make a sharp lefthand turn.6om8 a9p lwy6l ude .p6fynh,1