Section 11 – Rotational Motion
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Uniform Circular Motion
Circular Speed
Period and Frequency
Centripetal Acceleration
Centripetal Force
Vertical Circular Motion
Periodic Motion
Section 11.1
 Uniform Circular Motion
 Circular Speed
 Period and Frequency
Rotation vs. Revolution
An axis is the straight line around which rotation takes place.
 When an object turns about an internal axis—that is, an axis
located within the body of the object—the motion is called
rotation.
 When an object turns about an external axis, the motion is
called revolution.
Rotation vs. Revolution
The Ferris wheel turns about an
axis.
The Ferris wheel rotates, while the
riders revolve about its axis.
Rotation vs. Revolution
Earth undergoes both types of rotational motion.
• It rotates around an axis passing through its geographical
poles once every 24 hours.
• It revolves around the sun once every 365 ¼ days.
Uniform Circular Motion
Uniform Circular Motion
Uniform Circular Motion
Uniform circular motion is the motion of an object traveling
at a constant speed on a circular path.
Circular Speed
If an object travels at constant speed, that constant speed can
be found by taking the distance traveled and dividing by the
associated time of travel. (v=d/t).
Circular Speed: Distance
If the time that is used to calculate the constant speed is the
period, or time to complete one circular path, then the correct
distance to use would be the circumference of the circular path.
d  circumference  2r
Circular Speed: Time
There is a special time of travel that is of interest when the
motion of an object repeats itself.
This special time is called the period of the motion and is the
time required for the motion of the object to complete itself one
time.
Circular Speed: Time
In UCM, T (period) is the time, in seconds, to execute one complete
cycle of motion
Units:
sec / cycle (seconds per 1 cycle)
 Cycles can be laps, revolutions,
Circular Speed
To determine the constant speed of an object traveling in a
circular path in terms of the time (period) required for the object
to complete one circular path.
Hence, circumference divided by time is the speed of the object:
2r
v
T
r
Example #1
A girl drives her car clockwise around a circular track of radius
30 meters. She completes 10 laps around the track in 2 minutes.
Find her circular speed in m/s.
Example #2
A Nascar driver, traveling at a constant speed, completes a lap
around a circular track of diameter 320 meters in 36 seconds.
What is the circular speed of the car?
Example #3
A boy and a girl sit on a merry-go-round with a period of 3.5
seconds. The boy and girl sit 0.75 m and 0.35 m from the center
of the merry-go-round, respectively. Calculate the circular
speed of each child.
Period and Frequency
Period (T)
The time it takes for an object to make one complete cycle
(seconds)
Frequency (f)
The number of complete cycles of motion that occur in one
second
Units:
cycles / sec or Hertz (Hz) (Cycles per 1 second)
Period vs. Frequency Formulas
1
T
f
1
f 
T
Circular Speed expressed with period (T) or frequency (f)
2r
v
T
v  2rf
Example #4
Hamlet the hamster runs on his exercise wheel, which turns
every 0.5 seconds. What is the frequency?
Example #5
A sock is stuck on the inside of the clothes dryer spins around
the drum once every 2 seconds at a distance of 50 cm from the
center of the drum. What is the socks linear speed?
Example #6
What is the radius of an automobile that turns with a frequency
of 11 hertz and has a linear speed of 20 m/s?
Example #7
The wheel of a car has a radius of 0.29 meters and it being rotated at
13.83 hertz on a tire-balancing machine. Determine the speed at which
the wheel is moving.