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Homework answers / question archive / 1) A wrench is used to tighten a nut as shown in the figure

1) A wrench is used to tighten a nut as shown in the figure


1) A wrench is used to tighten a nut as shown in the figure. A 12-N force is applied 7.0 cm from the axis of rotation. What is the torque due to the applied force?

    1. 0.58 N • m
    2. 0.84 N • m  
    3. 1.71 N • m
    4. 14 N • m
    5. 58 N • m




2. A string is tied to a doorknob 0.79 m from the hinge as shown in the figure. At the instant shown, the force applied to the string is 5.0 N.


What is the torque on the door?

    1. 3.3 N • m
    2. 2.2 N • m
    3. 1.1 N • m
    4. 0.84 N • m
    5. 0.40 N • m






  1. A horizontal, 10-m plank weighs 100 N. It rests on two supports that are placed 1.0 m from each end as shown in the figure. How close to one end can an 800-N person stand without causing the plank to tip?
  1. 0 m                      (d) 0.6 m
  2. 0.2 m                   (e) 0.8 m  
  3. 0.5 m








4.      One end of a rope is tied to the handle of a horizontally-oriented and uniform door. A force F is applied to the other end of the rope as shown in the drawing. The door has a weight of 145 N and is hinged on the right. What is the maximum magnitude of F at which the door will remain at rest?


  1. 145 N                  (d) 424 N
  2. 265 N                  (e) 530 N
  3. 381 N




5. In the drawing shown, the large wheel has a radius of 8.5


m. A rope is wrapped around the edge of the wheel and a 7.6 kg-box hangs from the rope. A smaller disk of radius 1.9 m is attached to the wheel. A rope is wrapped around the edge of the disk as shown. An axis of rotation passes through the center of the wheel-disk system. What is the value of the mass M that will prevent the wheel from rotating?


  1. 1.7 kg                (d) 34 kg
  2. 3.8 kg                (e) 46 kg
  3. 12 kg






6. Consider four point masses located as shown in the sketch. The acceleration due to gravity is the same


everywhere. What is the x coordinate of the center of  gravity for this system?


  1. 2.0 m              (c) 3.0 m              (e) 3.8 m
  2. 2.7 m              (d) 3.3 m



7.  Consider the following four objects:         

                         a hoop;  a solid sphere; a flat disk;  a hollow sphere

Each of the objects has mass M and radius R. The axis of rotation passes through the center of each object, and is perpendicular to the plane of the hoop and the plane of the flat disk. Which object requires the largest torque to give it the same angular acceleration ?

  1. the hoop                               (d) the hollow sphere
  2. the flat disk                           (e) both the solid and the hollow spheres (c) the solid sphere




8. A massless frame in the shape of a square with 2-m sides has a 1-kg ball at each corner. What is the moment of inertia of the four balls about an axis through the corner marked O and perpendicular to the plane of the paper?


  1. 4 kg • m2
  2. 8 kg • m2
  3. 10 kg • m2
  4. 12 kg • m2
  5. 16 kg • m2




9.  The drawing shows the top view of a door that is 2 m wide. Two forces are applied to the door as indicated. What is the magnitude of the net torque on the door with respect to the hinge?

  1. 0 N • m       (c) 8.7 N • m       (e) 26.0 N • m  
  2. 5.0 N • m    (d) 10.0 N • m




10. Three children are pulling on a rotatable platform on a playground. The platform has a radius of 3.65 m. In the picture, two children are pulling with equal forces of 40.0 N in an attempt to make the platform rotate clockwise. The third child applies a force of 60 N as shown. What is the net torque on the platform? Note: “ccw” is counterclockwise and “cw” is clockwise.

  1. 73 N • m, ccw    (c) 511 N • m, ccw    (e) 0 N • m
  2. 73 N • m, cw       (d) 511 N • m, cw







11. A 45-N brick is suspended by a light string from a 2.0-kg pulley. The brick is released from rest and falls to the floor below as the pulley rotates through 5.0 rad. The pulley may be considered a solid disk of radius 1.5 m.

What is the angular speed of the pulley?

  1. 7.3 rad/s               (d) 15 rad/s
  2. 8.1 rad/s               (e) 17 rad/s
  3. 9.4 rad/s


12. Consider the following three objects, each of the same mass and radius:           


                            (1) a solid sphere (2) a solid disk (3) a hoop

All three are released from rest at the top of an inclined plane. The three objects proceed down the incline undergoing rolling motion without slipping. In which order do the objects reach the bottom of the incline?

(a) 1, 2, 3                 (c) 3, 1, 2                                (e) All three reach the bottom (b) 2, 3, 1                 (d) 3, 2, 1 at the same time.






 13. A 2.0-kg solid cylinder of radius 0.5 m rotates at a rate of 40 rad/s about its    cylindrical axis. What power is required to bring the cylinder to rest in 10 s?

(a) 20 W                      (c) 160 W                     (e) 400 W (b) 40 W                      (d) 200 W  


 14. A ceiling fan has five blades, each with a mass of 0.34 kg and a length of 0.66 m.      The fan is operating in its “low” setting at which the angular speed is 9.4 rad/s. If the blades can be approximated as uniform thin rods that rotate about one end, what is the total rotational kinetic energy of the five blades?

(a) 35 J                             (c) 23 J                            (e) 11 J (b) 29 J                             (d) 17 J  

15.  A 1500-kg satellite orbits a planet in a circular orbit of radius 6.2 × 106 m. What is      the angular momentum of the satellite in its orbit around the planet if the satellite completes one orbit every  1.5 × 104 s?

(a) 3.9 × 106 kg • m2/s             (c) 6.2 × 108 kg • m2/s       (e) 2.4 × 1013 kg • m2/s (b) 1.4 × 1014 kg • m2/s          (d) 8.1 × 1011 kg • m2/s


16.  A 3.0-kg ball moves in a straight line at 10 m/s as shown in the figure. At the instant shown, what is its angular momentum about the point P? (a) 30 kg • m2/s

  1. 90 kg • m2/s
  2. 120 kg • m2/s
  3. 150 kg • m2/s
  4. zero kg • m2/s

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