51) 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. Will the
spool roll toward you if the string is wound over the top of the spool
spindle? How about under the bottom of the spindle? 
CLICK
ON THUMBNAIL TO SEE DIAGRAM 
p51a & b. Spool with
thread over top (left) and over bottom (right) and colinear with lever
each of the two on the
left would cause rotation to the left, the third one would not rotate but
would slide to the left because there is no perpendicular force to the
lever arm 
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52)
Explain why a ball gains speed as it rolls down an incline in terms of
torque. Now explain why in terms of forces. 

Torque is created by the force of
gravity acting on the center of the ball which is not over the contact
point of support. This causes a Torque about the contact point resulting
in an angular acceleration down the incline.
The parallel component of the force
produced by gravity acting on the ball creates a torque around the contact
point, resulting in rotation. Friction is essential for rotation to occur
and its force is equal to the coefficient of friction multiplied by the
normal component of the weight of the ball. Without friction the ball
would slide down the incline rather than rotate. 
53) A
4kg ball is whirled on the end of a string that is 3 m long. The balls
linear speed 2mis. What is its angular momentum? 

Angular momentum
= Rotational Inertia x Rotational Speed = mass x linear velocity x
radius of rotation
= 4 kg x
3 m x 2 m/s = 24 kg  m^{2/}sec
Plug in the
numbers for your answer!! 
54) At the health spa,
Felix Flex finds that pulleys on the exercise machines are not circular,
but are “cams”  sort of oval shape. What do pulleys of this shape do to
the length of the lever arms and the forces exerted by the machine? 
CAM increases lever arm and multiplies
the forces
CLICK
FOR PICTURE 
55) A common thread
spool rests on a flat table. You gently puff 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 
If no rotation occurs the net torque
must be zero. Pulling at what angle from the lever arm would result in a
net torque of zero? See picture for #51 _{
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56) A meter stick is balanced at the 50cm
mark. You tie a 30N weight at the 30cm mark. Where should a 60N weight
be placed so the meter stick will again be balanced? 
CLICK
ON THUMBNAIL FOR DIAGRAM
TRY
the ANSWER OUT WITH THIS SIM !!!!! 
The hard
way 
An easier way 
ΣTorques =(30 N)
x (.5 .3 m) = (60 N) x (d  .5 m)
((30 N) x (.2 m) )/(60 N) = d (.5
m)
(.2m)/2 = .1 m = d .5m
(.1 + .5 )m = d
d = .6 m = 60 cm mark 
First move your
origin to the fulcrum
ΣTorques = 0
((30 N) x .2 m))  ( (60 N) x d_{from fulcrum}) = 0_{
}(30 N) x .2 m = (60 N) x (d_{from fulcrum})_{
}(30/60) x (.2m) = d_{from fulcrum
}(.5) x (.2m) = d_{from fulcrum
}d_{from fulcrum}= .1 to right of center
or at the 60 cm mark 

57) A ring, a disk, and
a solid ball having equal masses roll down a hill at the same time. Which
reaches the bottom first? Why? 
click on thumbnail for picture
For why? and
mathematical explanation go here 
58) 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, would your linear speed be different? How about your angular speed? 
Linear speed would be less, angular
speed the same 
59) When a gymnast moves
from an extended position to a tucked position, how does her rotational
inertia change? 
Rotational Inertia is proportional to
the square of the radius and dancers reduce their Inertia by tucking
in their arms and/or legs. This increases their rotational speed through
the conservation of Angular momentum = Rotational Inertia x Angular
Velocity, The law of conservation of angular momentum tells us that
decreasing their Rotational Inertia will increase their Angular Velocity
(spin rate) To decrease Inertia they can pull their hands and arms into
their body from an extended position. Gymnasts, skaters, skiers, dancers
all do some variation of this to either increase of decrease their speed
of rotation for specific moves. also tuck their knees into their chests
while doing tumbling and other aerials. Same answer for questions #77,
59,64 
60) Solid cylinders will
roll down an incline with greater acceleration than hollow cylinders. What
is the effect of mass and diameter on this? Is there some combination of
diameter and mass that will result in a solid cylinder accelerating less? 
No effect. No.
mathematical
explanation go here _{
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61) Which rolls to the bottom of a hill
sooner, an empty car tire or same tire mounted on a rim? 
A tire is a ring or hoop, with the
wheel inside of it becomes a disk or cylinder. Tire on rim will be faster
For rest of answer see
# 57. 

62) A ring and a disk roll down a hill
together which reaches the bottom first? 
Disk.
mathematical explanation go here 
63) If the planet Jupiter underwent
gravitational collapse, what would happen to its rate of rotation about
its axis? 
Radius decreases, what would the
rotational speed do to maintain momentum 
64) When an ice skater pulls
in his hands while in a spin what happens to his moment of inertia? His
angular momentum? His rotational speed? 
Rotational Inertia is proportional to
the square of the radius. Athletes and dancers reduce their Inertia by
tucking in their arms and/or legs. This increases their rotational speed
through the conservation of Angular momentum = Rotational Inertia x
Angular Velocity, The law of conservation of angular momentum tells us
that decreasing their Rotational Inertia will increase their Angular
Velocity (spin rate) To decrease Inertia they can pull their hands and
arms into their body from an extended position. Gymnasts, skaters, skiers,
dancers all do some variation of this to either increase of decrease their
speed of rotation for specific moves. also tuck their knees into their
chests while doing tumbling and other aerials. Same answer for questions
#77, 85, 59 
65) Which has less
rotational inertia, a girl running with her legs bent or the same girl
running with her legs straight? 
Rotational Inertia is proportional to
the square of the radius. Athletes and dancers reduce their Inertia by
tucking in their arms and/or legs. This increases their rotational speed
through the conservation of Angular momentum = Rotational Inertia x
Angular Velocity, The law of conservation of angular momentum tells us
that decreasing their Rotational Inertia will increase their Angular
Velocity (spin rate) To decrease Inertia they can pull their hands and
arms into their body from an extended position. Gymnasts, skaters, skiers,
dancers all do some variation of this to either increase of decrease their
speed of rotation for specific moves. also tuck their knees into their
chests while doing tumbling and other aerials. Same answer for questions
#77, 64, 85, 59 _{
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80 85 END} 
66) Two people sit on a balanced seesaw. When
one person leans toward the center of the seesaw, what happens to that
person’s end of the seesaw? Why? 
Decrease Torque and create imbalance
making that person's end rotate up 
67) The resistance an object has to changes
in its rotational state of motion is called rotational______________ 
INERTIA click here for
definition 
68) If a football is kicked
so the force on the ball is through its center of gravity, will the ball
tumble or move without tumbling? Explain why. 
In theory yes, but in reality, your
foot is moving in a circular path and it would be impossible to follow
through in a perfectly linear manner. If you see this on the exam the
answer is still 'YES' 
69) Will an object always change its angular
momentum when acted on by an unbalanced force? 
NO, only if that force produces a
TORQUE 
70) Which has more
rotational inertia, a bicycle wheel or a solid disk of the same mass and
diameter? 
Bike wheel can be considered a hoop a solid
disk is a cylinder.
For rest of answer and mathematical
explanation go here For diagram go to #57
_{
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71) Define angular momentum.
Rotational Inertia x
Angular Velocity = mvr for concentrated mass. (ball on
string, hoop) 
click here for
definition Hyperphysics
 Angular Momentum 
72) Which will roll down an incline with
the greatest acceleration, objects with large rotational inertias or
objects with small rotational inertias? 
SMALL ROTATIONAL INERTIAS WILL BE
FASTER IN GENERAL BUT IS ACTUALLY ROTATIONAL INERTIA PER UNIT MASS THAT
DETERMINES
For solution & mathematical explanation go
here 
73) To turn a stubborn
screw, it is best to use a screwdriver that has a long handle, or one that
has a wide handle? Why? 
probably at THandle or even better
yet, a bit in a power driver! 
74) Is a person’s rotational inertia is
least about his longitudinal, transverse, or median axis? 
LONGITUDINAL. Median and Transverse
would be approximately equal.
Look in your book, section 11.5
CLICK
FOR PICTURE 
75) Suppose you try
loosening a nut with a wrench, and the nut doesn’t give at all. Can you
increase your chance of success if you use a longer wrench? If you exert a
larger force? Make sure that you are pushing perpendicular to the wrench?
Explain your reasoning in each case. 
YES, more torque. YES, more torque.
Yes, if force was not all perpendicular part of it was being wasted. Y
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76) Torque is defined as __________
Produce of Perpendicular force and
length of lever arm 
click here for
definition HyperPhysics
 Torque 
77) Suppose a huge rotating cloud of
particles in space gravitates together to form a dense ball. As the cloud
shrinks in size what happens to its rate of rotation? 
Angular momentum = Rotational
Inertia x Angular Velocity, to conserve momentum (to keep it from
changing), as the cloud gets smaller (its rotational inertia gets smaller)
its Angular Velocity must increase 
TRUE/FALSE. If true, mark “A”, If
false, mark “B” on the Scantron 
78) How can Ice skaters
increase their spin rate by using the conservation of angular momentum? 
Angular momentum = Rotational Inertia
x Angular Velocity, conservation of angular momentum tells us that
decreasing their Rotational Inertia will increase their Angular Velocity
(spin rate) To decrease Inertia they can pull their hands and arms into
their body from an extended position._
Skating
video (avi 565 kb)
Skating Video (avi 850
Kb)
Rotational Inertia is
proportional to the square of the radius. Athletes and dancers reduce
their Inertia by tucking in their arms and/or legs. This increases their
rotational speed through the conservation of Angular momentum = Rotational
Inertia x Angular Velocity, The law of conservation of angular momentum
tells us that decreasing their Rotational Inertia will increase their
Angular Velocity (spin rate) To decrease Inertia they can pull their hands
and arms into their body from an extended position. Gymnasts, skaters,
skiers, dancers all do some variation of this to either increase of
decrease their speed of rotation for specific moves. also tuck their knees
into their chests while doing tumbling and other aerials. Same answer for
questions #78, 59, 64, 85 
79) In order for a seesaw to be in
rotational equilibrium, must the torques acting on it be balanced? Do the
riders have to sit equidistant from the fulcrum ? 
In other words if you weigh 150
pounds and another person weighs 100 pounds and you both sit at the same
distance from the center of the seesaw will it be balanced (in rotational
equilibrium)? 
80) A spinning wheel will
maintain its state of angular momentum unless acted on by what? 
click here for law of
conservation of angular momentum _{
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81) Define rotational inertia.
Property of an object or system use to
quantify how it resists changes to its rotational state. 
click here for
definition 
82) If you kick a football near one of its
ends, will it tumble as it sails through the air? Why? 
YES, You created a torque 
83) Does a short pendulum have more
rotational inertia than a long pendulum of the same mass? Explain. 
Rotational Inertia for
concentrated mass (weight at end of pendulum) is = mr^{2} 
84) Define torque 
click here for
definition 
85) How can gymnasts
change their rotational inertia while going through gymnastic routines? 
Rotational Inertia is proportional to
the square of the radius. Athletes and dancers reduce their Inertia by
tucking in their arms and/or legs. This increases their rotational speed
through the conservation of Angular momentum = Rotational Inertia x
Angular Velocity, The law of conservation of angular momentum tells us
that decreasing their Rotational Inertia will increase their Angular
Velocity (spin rate) To decrease Inertia they can pull their hands and
arms into their body from an extended position. Gymnasts, skaters, skiers,
dancers all do some variation of this to either increase of decrease their
speed of rotation for specific moves. also tuck their knees into their
chests while doing tumbling and other aerials. Same answer for questions
#78, 59, 64. Gymnasts also tuck their knees into their chests while doing
tumbling and other aerials.

86) Name two ways that a tightrope walker
can increase his rotational inertia. 
hold a long pole in your hands.
Ever see a picture of one with a long bar in his hands. See
Niagra Falls picture below.
click
to see full size 
87) What is the name of the distance
between a turning axis and the point of contact of a perpendicular force? 
LEVER ARM.
click here if you still don't
know 