12.43: Several forces act on a rigid body. If the resultant (net) force on the r.3rj yc7g6bsj8ks t(body is zero, which one of the following statementsksg.6j rbs( cy jt7r38 must be true?

  97.39: A cylinder free to turnaround a fixed axis has d uzxy2 j9v nq.7b6.t3ytehx9a string wrapped around it as shown to the right9tbdu jhy693vqx7t . .en zx2y. 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 xlg+9i.yn hm3 about an axis through its center. The stick starts fro i9h3n.myxgl +m 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 b:nlg n-isd5p4h v2i (glade has kinetic energy K when rotating with constant angular velocity. When the angular velocity is reduced to one-third, the5ps2gli-hn g(d:in4 v kinetic energy becomes

  12.33: A solid, uniform sphere rolls without slit)j*grq 21p/3,f ljb6 m pzgtepping 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 r, and rotational inerti:yttf,jt1 9t fj21m qha $0.5m{r}^2$ . 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 have a4qt7z (6m urdmass M and radius R. Each object begins purely rolling without slipping down a rough inclined plane. The coefficients of friction for the di4atzdqmr(6 u7sk and ring with the incline are ${\mu }_{d}isk>{\mu }_{r}ing$.
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 diu4n5ieal ,uqhv4f:( ksk 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 hq: u4vu5, neaf k4(liring with the incline are ${\mu }_{d}isk>{\mu }_{r}ing$.
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 slippingd2ewzvr5 ,l0*or d(j x on a rough inclined plane. Which one of the following o0e5d ,dr(2x*j zrv wlchoices 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 length L is pfgyq:t r: +s*uxsw*+iivoted about its left end. It is released from an angle θabove the horizontal. What is the magnitude of the angula qftg:*x+swy su*i:r +r acceleration of the rod about the pivot when the rod is released?

  15.46: A uniform rod of mass M and leng9tp:vt7g n1ey th L is fixed to rotate about a frictionless ppnteyv7g9 : t1ivot 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 of mass M and length L im+1ux . tlp ;sb/ e)pc+1pey/sul.htas fixed to rotate about a frictionless p txs epup+scby1ea ;mhlp.// 1tul+.)ivot located L/3 from one end. The stick 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 vertically each of three long unimte4r.dkeiz1jx*jiff4 z 69i (9v8msform cylinders with equal radii on e1fkej xz89v miijmt 69.i4(f r*4zdsthe 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 disk x kdmoy9jv *26bh cf))57joizs,X 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 ma a )x-uy;yxah:ss each are mounted to rotate about an axis fixed through the center of the disk. Each disk isx;-ah ua):yxy 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 massesd;f wd+h* n yq1exj9fn.z 5 q37rp*tak M but different radii such thatx+fyr*d; fnhq a ez.w53jd7qp1kn* 9t $r_x<r_y$. 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 radi i64tqkrhc :t;us R is pulled by a horizont t;tic r:qk64hal 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 rotates clockwise awd8g 7zjnw/6rmfi ;5s bout its center with an az/ rn67 gj ;swm8f5dwingular speed ${\omega }_0$ . 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 c-d(3wntlt b gup;8eh8 ylinder 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 cde -tl 8bg wpnu(8t3;hylinder 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 e/o7mju)n rl f2jsy:z 9 gn)qb2ngine plane are turning in a clock wise direction with respect to the pilot. The gnqjm)y2 s:79f 2jnr/ )ouzblgyroscopic action of the moving parts will cause the plane to move in which direction as the pilot tries to make a sharp lefthand turn.