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Chapter 8
Rotational Motion
1. CIRCULAR MOTION
• Which parts on a merry-go-round move fastest?
• Which have greater rotational speeds?
• Examples of rotational motion:
Earth rotates and revolves
2. ROTATIONAL INERTIA
• Law of inertia for rotating systems
An object rotating about an axis tends to remain
rotating at the same rate about the same axis unless
interfered with by some external influence.
• Examples: bullet, arrow, and earth
•
•
•
•
•
Demo – Football and Spinning Basketball
Demo - Whirly Tube (Zinger)
Demo – Whirly Shooter
Demo - Disc Gun
Demo - Rubber Bands
• Demo - Inertia Bars
• Moment of inertia (rotational inertia)
The sluggishness of an object to changes in
its state of rotational motion
• Distribution of mass is the key.
• Example: Tightrope walker
• Demo - Ring and Disk on Incline
• Demo – Metronome
• Walking pendulums (bending knees)
• Demo – Falling Meter Sticks
Lecture
Table
3. TORQUE
• Rotational analog of force
• A torque changes the rotational state of
motion.
• Torque = force x lever arm length
• It is a vector.
• Units - N.m or lb.ft
See-Saw
F
D
D=F
D
D
F
D=F
D
( 50 lb )x  150 lb( 2 ft )
(50 lb ) x  300 lb  ft
x  6 ft
150 lb
50 lb
x
2 ft
l
= Fl
Torque = Fl
l
Cheater Pipe
Torque
Torque = Fl
F
F
Line of action of the force
F
4. CENTER OF MASS AND
CENTER OF GRAVITY
Center of mass - average position of mass
Center of gravity - average position of weight
..
Earth
Very large meteor
Path of center of mass of a rotating object will
be a straight line if no external forces act on
the object.
Demo – Hammer Toss
Locating the Center of Gravity
•
•
•
•
•
Demo – Meter Stick
Demo - Map of Texas
Demo - Balancing Eagle
Demo - Curious George
Demo – Picking Up Candy
• Center can be outside of the object.
• Examples: high jump and pole vaulting
Stability
• Demo - Tower of Pisa
• Demo - Touching Toes
• Demo - Standing on Toes
• Demo - Object Rolling Uphill
• Video – Dog Center of Mass
• Demo - Boards Over the Edge
1/2
1/4
1/6
1/8
Equilibrium - Unstable
If an object is displaced slightly from equilibrium and
released and the object moves to a new position, then
the object was in a state of unstable equilibrium.
Example: Ball on inverted bowl
Equilibrium - Stable
If an object is displaced slightly from equilibrium and
released and the object returns to its old position,
then the object was in a state of stable equilibrium.
Example: Ball in bowl
Equilibrium - Neutral
If an object is displaced slightly from equilibrium and
released and the object remains where it is, then it
was in a state of neutral equilibrium.
Example: Ball on horizontal surface
5. CENTRIPETAL FORCE
• Centripetal force - center seeking force
• Examples: tin can and string, sling, moon
and earth, car on circular path, flying cat
• Demo - Coin on Clothes Hanger
• Demo - String, Ball, and Tube
• Demo - Loop the Loop
6. CENTRIFUGAL FORCE
• Centrifugal force - center fleeing force
• Often confused with centripetal
• Examples: sling and bug in can
• Demo - Walk the Line
• Centrifugal force is attributed to inertia.
7.
CENTRIFUGAL FORCE
IN A ROTATING
REFERENCE FRAME
• A frame of reference can influence our view
of nature.
• For example: we observe a centrifugal
force in a rotating frame of reference, yet it
is a fictitious (pseudo) force.
• Centrifugal force stands alone (there is no
action-reaction pair) - it is a fictitious force.
• Another pseudo force - Coriolis
8. SIMULATED GRAVITY
• To get a = g, the proper rotation rate and the
proper radius must be determined.
• Gravity gradients
• Jogging in space
9. ANGULAR MOMENTUM
For a point object the angular momentum is
v
J = mvr
Units - kg.m2/s or sl.ft2/s
It is a vector.
Here the vector is pointing toward you.
m
r
• How do you change the angular momentum
of an object?
• An external torque is required.
• Newton's first law for rotating systems:
An object or system of objects will maintain
its state of angular momentum unless acted
upon by an unbalanced external torque.
• The larger J is, the larger the torque must be
to change it.
• Demo - Bicycle Wheel
• Demo - Gyroscope
10. CONSERVATION OF
ANGULAR MOMENTUM
• If there are no external torques acting on a
rotating system then
angular momentum is conserved.
• This means the final angular momentum is
equal to the initial angular momentum.
• Examples: ice skater spin, diving, tides and
moon
I  I
• Demo - "Ice Skater“
• Movie – Ice Skater
• Movie – SFA Cheerleaders
• Demo - Bicycle Wheel and Rotating Platform
• Movie - J in Sky Lab
• Movie - More J in Sky Lab
Chapter 8 Review Questions
In walking, people normally bend their
knees. Why?
(a) it is easier to swing their legs because
bending lowers the rotational inertia of
their legs
(b) it is easier to swing their legs because
bending increases the rotational inertia of
their legs
Which is harder to stop? A rotating rod
with its mass predominantly at the
(a) middle of the rod
(b) ends of the rod
(c) neither of the above
A ball is at rest on a horizontal table. It is
in a state of
equilibrium.
(a) neutral
(b) stable
(c) unstable
(d) both (a) and (b)
(e) both (a) and (c)
Which of the following forces is a
pseudo force?
(a) tension in a rope
(b) force of gravity
(c) centripetal
(d) friction
(e) centrifugal
What is the angular momentum of a 6 kg mass
traveling with a speed of 6 m/s in a circle of
radius of 12 m?
(a) 432 kg·m2/s
(b) 12 kg·m2/s
(c) 24 kg·m2/s
(d) 144 kg·m2/s
(e) 36 kg·m2/s