Choose the best answer to each question and write the appropriate letter in the space provided.

1)  Torque is defined as __________.
A)mass times velocity
B)force times time
C)force times lever arm
D)mass times acceleration
E)momentum times radius

2)  Suppose you try loosening a nut with a wrench, and the nut doesn't give at all. You increase your chance of success if you __________.
A)extend the lever arm
B)be sure to exert force perpendicular to the lever arm
C)exert a larger force
D)have a friend help you pull on the wrench
E)all of the above

3)  If a football is kicked so the force on the ball is through its center of gravity, the ball will __________.
A)tumble end over end in the air
B)spin about its axis in the air
C)move without any tumbling or spinning
D)not even get into the air
E)deflate

4)  The resistance an object has to changes in its rotational state of motion is called rotational __________.
A)momentum
B)inertia
C)torque
D)acceleration
E)velocity

5)  Which has more rotational inertia, a bicycle wheel or a solid disk of the same mass and diameter?
A)The wheel.
B)The disk.
C)They both have the same rotational inertia.

6)  Which has more rotational inertia, a girl running with her legs bent or the same girl running with her legs straight?
A)With bent legs.
B)With straight legs.
C)Both have the same rotational inertia.

7)  Which objects roll down an incline with the greatest acceleration?
A)Objects with large rotational inertia.
B)Objects with small rotational inertia.
C)Acceleration is independent of rotational inertia in this case.

8)  Any solid cylinder will roll down an incline with greater acceleration than any hollow cylinder if the __________.
A)mass of the solid cylinder is large
B)diameter of the solid cylinder is large
C)mass of the solid cylinder is small
D)none of the above are necessary

9)  A person's rotational inertia is least about __________.
A)the person's longitudinal axis
B)the person's transverse axis
C)the person's median axis
D)an axis through the person's hands
E)an axis through the person's feet

10)  When a gymnast moves from an extended position to a tucked position, she __________.
A)decreases her rotational inertia
B)decreases her rotational inertia
C)neither A nor B

11)  Angular momentum is defined as __________.
A)mass times velocity
B)rotational inertia times linear velocity
C)momentum times rotational velocity
D)none of the above

12)  An object will maintain its angular momentum unless acted on by an unbalanced force.
A)Always true
B)Sometimes true
C)Always false

13)  When an ice skater pulls in his hands to turn faster __________.
A)angular momentum must be conserved
B)his moment of inertia changes
C)his rotational speed changes
D)all of the above

14)  If the planet Jupiter underwent gravitational collapse, its rate of rotation about its axis would __________.
A)decrease
B)increase
C)stay the same
D)More information needed.

15)  Suppose a huge rotating cloud of particles in space gravitates together to form a dense ball. As the cloud shrinks in size it rotates __________.
A)faster
B)slower
C)at the same speed

16)  Two people sit on a balanced seesaw. When one person leans toward the center of the seesaw, that person's end of the seesaw will __________.
A)rise
B)fall
C)stay at the same level

17)  To turn a stubborn screw, it is best to use a screwdriver that has a __________.
A)wide handle
B)long handle
C)yellow color
D)none of the above

18)  Suppose a carnival Ferris wheel has seats that are located halfway between the center and the outside rim. Compared to the ordinary Ferris wheel, where the seats are on the outside rim, your angular speed on this Ferris wheel would be __________.
A)less
B)more
C)the same

19)  Which rolls to the bottom of a hill sooner, an empty car tire or the same tire mounted on a rim?
A)The mounted tire, provided the tire is more massive than the rim
B)The mounted tire, provided the tire is lighter in weight than the rim
C)The mounted tire, regardless of its weight
D)The empty tire, provided it is as heavy as the rim
E)The empty tire, regardless of its weight

20)  A ring and a disk roll down a hill together. Which reaches the bottom first?
A)The ring
B)The disk
C)Depends on the masses
D)Depends on the moments of inertia
E)Both reach the bottom at the same time

21)  A good explanation of why a ball gains speed as it rolls down an incline involves the __________.
A)force that acts on it
B)torque that acts on it
C)friction between it and the incline
D)concentrated rotational inertia of the ball
E)all of the above

22)  At the health spa, Felix Flex finds that pulleys on the exercise machines are not circular, but are "cams" -- sort of oval-shape. At different orientations, the cams provide different __________.
A)lengths of lever arms
B)forces required to produce a given torque
C)both A and B
D)none of the above

23)  A common thread spool rests on a flat table. You gently pull in a horizontal direction on a short piece of thread attached to (wrapped around) the spool.  The spool will roll toward you __________.
A)only if the string is wound over the top of the spool spindle
B)only if the string is wound under the bottom of the spool spindle
C)whether the string is wound over or under the spool

24)  A common thread spool rests on a flat table. You gently pull at an angle on a short piece of thread attached to (wrapped around) the spool that causes the spool to slide without rotating. With the thread at this angle, the lever arm is __________.
A)small, but not zero, and the torque is zero
B)small and the torque is also small
C)perpendicular to the applied force
D)none of the above

25)  A meter stick is balanced at the 50-cm mark. You tie a 20-N weight at the 30-cm mark. Where should a 30-N weight be placed so the meter stick will again be balanced?
A)20 cm mark
B)30 cm mark
C)50 cm mark
D)70 cm mark
E)80 cm mark

26)  A 2-kg ball is whirled on the end of a string that is 3 m long. The ball's linear speed is 2 m/s. What is its angular momentum?
A)24 kg\'97m\'97m/s
B)12 kg\'97m\'97m/s
C)6 kg\'97m\'97m/s
D)4 kg\'97m\'97m/s
E)3 kg\'97m\'97m/s

27)  A ring, a disk, and a solid ball having equal masses roll down a hill at the same time. Which reaches the bottom first?
A)The ring
B)The disk
C)The ball
D)Depends on what each is made of.
E)Depends on the radius of each.

Write True or False in the space provided.

28)  The distance between a turning axis and the point of contact of a perpendicular force is called the fulcrum.
29)  Torque is the product of a force exerted on an object times the lever arm.
30)  Rotational inertia is the resistance an object has to changes in its rotational state.
31)  In order for a seesaw to be in rotational equilibrium, the sum of the torques acting on it need not be balanced if one person sits closer to the fulcrum than the other person.
32)  If you kick a football through its center of gravity it will tumble as it sails through the air.
33)  In order to increase his or her rotational inertia, a tightrope walker can carry a long stick.
34)  A short pendulum has more rotational inertia than a long pendulum of the same mass.
35)  Gymnasts change their rotational inertia while going through gymnastic routines.
36)  A spinning wheel will maintain its state of angular momentum unless acted on by an external torque.
37)  Ice skaters can increase their spin rate by using the conservation of angular momentum.

On a separate sheet of paper, answer the following questions.

38)  Define torque. When all the torques on an object are balanced, the object is in rotational equilibrium. Apply this statement to two people sitting on either side of a seesaw. Give an example.
39)  In terms of torques and center of gravity, explain why you fall over if you try to touch your toes while your heels are against a wall.
40)  In terms of rotational inertia, explain why a tightrope walker gains stability when carrying a long pole.
41)  Which has more rotational inertia, a solid sphere of mass 100 kg and radius 50 cm or a solid cylinder of the same mass and radius? What is the rotational inertia of the sphere?
42)  Define angular momentum. Discuss how conservation of angular momentum is applied to a gymnast starting from a standing position and turning a somersault in the air. Consider the change in his or her rotational inertia.

Answer the following questions in the space provided. Show all work.

43)  Suppose the torque produced by a wrench on a stubborn nut is  20 N m. If the lever arm is tripled with no change in force, what is the resulting torque?
44)  A 60-kg boy sits on a seesaw 1.0 m from the fulcrum. What distance from the fulcrum should a  30-kg girl should sit in order to balance the seesaw?
45)  Consider a long uniform wooden plank of weight  W resting on a table. The left end of the plank can extend beyond the table without toppling as long as the CG of the plank rests on the table. If the CG extends beyond the table's edge, then a weight placed on its right end can prevent toppling. How much weight would prevent toppling if 3/4 of the plank extended beyond the edge?
46)  A ball at the end of a long rope is swung into a horizontal circular path. The rope is then pulled in so that the radius of the path is 1/ 3 as big. How does the tangential speed of the ball change?