12.43: Several forces ac:xsflhlpbh-piyn :98);y ; g ht on a rigid body. If the resultant (net) force on the body is zero, which one of the followilnfh p y:sp; )8hhgyxli9;-:bng statements must be true?

  97.39: A cylinder free to turnaround a fixed axis has a sg7d d03.ocrtktring wrapped around it as showndgcok.t 0d r37 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 axis throug kbg)0k6q;hu oh its center. The stick starts from res q60bgok hku;)t 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 d:m n9glb)l.s4sneu 4rotating with constant angular velocity. When the angular vel4esn :n4bdg9.lm)s u locity is reduced to one-third, the kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slipping on c: c f u8r8:6icpe)nakm5u d,fa 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 inerti:f3 m l( ..dcu/ps5kdol* w:l6hz xntza $0.5mr^{2}$ . 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 b(ewnxxz4 g59 solid disk and 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 wzxbxe49 5g(n 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 have mass M anh,vy8sf xf+ :9rk jxx-qmg,c1d radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of friction for the disk s9mqxg xk x 1-h:+,,8cjfvfry 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 pf5kc9wuxe8( rolls without slipping on a rough inclined plane. Which one of the 59(xf pkuwec8 following choices best represents the type and direction of friction (if any) acting on the cylinder as it rolls up the incline?

  14.43: A long rod of lengthbj -7k rw+c omd0jpa25 L is pivoted about its left end. It is released from an angle θabove the horizontalm jrjb5oda0wk+p-c 72 . 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 rott/ zi2 qw ud.3b-vbu4cate 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 the magnitude of the tangential acceleration of its /.tbu3czv-wqu4dbi2 center of mass?

  16.50: A uniform stick of mass M and length L is fixed to rotate a/c+ se2xlgu5ou ui3rbx*(yk59 vj; ld bout a frictionless pivot located L/3 from one end. The stick r9+5e5 dkxusuv cxli;ylg*/j 2(bu3o is 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 verticalll+hl e 47nf6jry each of three long uniform cylinders with equal radii on the end of his finger:+llhfr4 jn76e
• 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,X6g oyne0 9:hax9 yjucqs+1b6s 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 di ve0j:9dik3rm sks of equal mass each are mounted to rotate about an axis fixed through the center of kir0 9dv e:3jmthe 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 equaei/-hq49 sdmz* x1png qai8,b l masses M but different radii such that-d8 mpqesnxz9a*hq 1 gi/i4b, $r_x< r_y$. 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 pulled by bt.m)6fkg ji59vx z/oa horizontal k6 )9bmgzt.xjfvo /i5force 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 clo 3y (aehbt::n 4v)ju hp+:ggbqckwise about its center with an angulab:(nev)hjbugg:43 +:a tqp hyr 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=10.0 cm i eub.qnriu;1k.t1,+ 4mo 0grwq qrt9es connected about an axis through the center of the c n ei,0w+quq14r.oe;m1rr kq. 9gubtt ylinder 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 a single /sm0zl. zmw+ w50 z2tnzih7avengine plane are turning in a clock wise direction with respect to the pilot. The gyroscopic action of the moving parts will caus2 7.i 5w/w mt+n0hsmzv 0zlzaze the plane to move in which direction as the pilot tries to make a sharp lefthand turn.