Circular Motion

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Circular Motion
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What is circular motion?

• Anything that rotates or revolves around a
  central axis is in circular motion.

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Rotation vs. Revolution
An axis is the straight line around which
rotation takes place.

• Rotation an object turns about an internal
  axis. Spinning
• Revolution an object turns about an external
  axis, Turning

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Rotation vs. Revolution

• The Ferris wheel turns about an axis.
• The Ferris wheel rotates, while the riders
  revolve about its axis.

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Rotation vs. Revolution

• Where is rotation?
• Where is revolving?

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Uniform Circular Motion

• is the motion of an object in a circle with a
  constant or uniform speed.

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We have been referring to constant speed. How
would you describe the velocity?

• Remember velocity is a vector quantity so has
  magnitude and direction

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• Velocity of Uniform Circular Motion
• constant magnitude
• changing direction-always tangential to the circle

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Miniature golf where will the golf ball
go?Over point A, B, or C?
A
C
B
B
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As an object moves in uniform circular motion
(remember speed is constant) is there
acceleration?

• Yes
• Although speed is constant, velocity is not!!!
• Acceleration is a change in velocity
• It is accelerating because the direction of the
  velocity vector is changing.

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Identify the three controls on an automobile
which allow the car to be accelerated.
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In uniform circular motion, what is the direction
of the acceleration?
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conditions for uniform circular motion

• The velocity vector and the acceleration vector
  are always perpendicular to each other.
• The acceleration vector changes only the
  direction of the velocity vector not the
  magnitude of it.
• The acceleration vector is directed inwards

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conditions for uniform circular motion
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• In circular motion, what is the direction of the
  velocity vector?
• In circular motion, what is the direction of the
  acceleration vector?
• Question to think about
• You are riding the carousel at the Woodlands
  Mall. How long does it take to make a complete
  circle? How many times does it do this in a
  second? Are these related?

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What does it mean to be periodic?
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Period vs Frequency

• T Period
• Time for one cycle or revolution (seconds)
• f Frequency
• Number of cycles or revolutions per second (hertz
  or sec-1)

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Formulas Calculating Period and Frequency
T period or time for one revolution (sec) f
frequency or revolutions per second (Hz or
sec-1)
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FormulasThe period is inversely proportional to
the frequency

• T period or time for one revolution (sec)
• f frequency or revolutions per second (Hz or
  sec-1)

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Example 1

• A merry-go-round makes 6 revolutions in 10
  seconds. What is its frequency?

The definition of frequency is the number of
revolutions per second
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Example 2

• A merry-go-round makes 6 revolutions in 42
  seconds. What is its period?

The definition of period is time required to
complete one revolution
T 42sec/6rev The period is 7
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Example 3

• A merry-go-round has a frequency .5Hz. What is
  its period?

T 1rev/.5HZ Period 2sec
Remember Hz revolutions/sec
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If we know time of 1 revolution (T), How do we
determine velocity of 1 revolution?

• We will consider velocity at a point tangent to
  the circle
• Velocity d/t
• For distance dependent on the circumference of
  the circle
• d 2?r (distance of 1 revolution)
• t T (time of 1 revolution)
• Together

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Calculating speed

• v speed (m/s)
• r radius of circle (m)
• T period or time for one revolution (sec)
• f frequency

OR
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Example 4 A lifeguard twirls her whistle on a
string in a horizontal circle with a radius of
0.34 m. It takes 1.5 second to complete the
circle. What is the average tangential speed of
the whistle?

• Given

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Example 4 A lifeguard twirls her whistle on a
string in a horizontal circle with a radius of
0.34m. It takes 1.5 second to complete the
circle. What is the average tangential speed of
the whistle?

• Given r 0.34 m
• T (1.5 sec /1rev) 1.5 sec/rev

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Example 4 A lifeguard twirls her whistle on a
string in a horizontal circle with a radius of
0.34 m. It takes 1.5 second to complete the
circle. What is the average tangential speed of
the whistle?

• Given r 0.34 m
• T (1.5 sec /1rev) 1.5 sec/rev

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• the average speed and the radius of the circle
  are ________ proportional.
• A twofold increase in radius corresponds to a
  _______ increase in speed if period remains the
  same

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Example 5 A lifeguard twirls her whistle on a
string in a horizontal circle with a radius of
28 cm. It takes 4.8 second to revolve 5 times.
What is the average tangential speed of the
whistle?

• Given
• r T

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Example 5 A lifeguard twirls her whistle on a
string in a horizontal circle with a radius of
28 cm. It takes 4.8 second to revolve 5 times.
What is the average tangential speed of the
whistle?

• Given r 28 cm 0.28 m
• T (4.8 sec /5rev) 0.96 sec/rev

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Example 5 A lifeguard twirls her whistle on a
string in a horizontal circle with a radius of
28 cm. It takes 4.8 second to revolve 5 times.
What is the average tangential speed of the
whistle?

• Given r 28 cm 0.28 m
• T (4.8 sec /5rev) 0.96 sec/rev

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As an object moves in a uniform circle

• What happens to its speed?
• What happens to its velocity?
• What happens to its acceleration?

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Formulas Calculating Centripetal Acceleration
using speed

• ac centripetal acceleration (m/s2)
• r radius of circle (m)
• v speed (m/s)

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What causes an object to have Centripetal
Acceleration?

• Centripetal Force NOT centrifugal force
• Whats the difference?
• Centripetal center seeking
• Centrifugal outward seeking

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Without a net centripetal force, an object cannot
travel in circular motion. In fact, if the forces
are balanced, then an object in motion continues
in motion in a straight line at constant speed.
With a centripetal force, an object in motion
will be accelerated and change its direction.
Without a centripetal force, an object in motion
continues along a straight-line path.
Courtesy http//www.physicsclassroom.com/mmedia/ci
rcmot/cf.cfm
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frame of reference

• Centripetal forces are those seen by an observer
  in an inertial frame of reference.
• Centrifugal forces are those felt by an observer
  in an accelerating frame of reference. As a car
  goes around a corner, the passengers think they
  feel a force towards the outside of the curve, in
  reality this is due to inertia. Centrifugal force
  is a misnomer!!!

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What causes centripetal acceleration?

• To have acceleration, there must be a net force
  towards the center of the circle
• What is the force for the following
• Earth circling the sun
• Force of Gravity
• Car turning a bend
• Force of Friction
• Xena warrior princess throwing a ball on a chain
• Force of Tension on chain

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Formulas Calculating centripetal force using
centripetal acceleration

• Fc centripetal force (N)
• m mass (kg)
• ac centripetal acceleration (m/s2)

OR
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Example 6

• A little girl is swinging her 5 kg purse in
  horizontal circles using the strap that allows
  the purse to swing 20 cm from her hand. The girl
  is able to get the purse to make 10 revolutions
  in 8 seconds. What was the speed of the purse?
  What is the centripetal acceleration of the
  purse? How much tension is in the purse string?

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Example 6

• Given
• m r T

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Example 6 determine velocity

• Given m 5 kg r 20 cm 0.2 m
• T (8sec / 10rev) 0.8 sec/rev

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Example 6 determine velocity

• Given m 5 kg r 20 cm 0.2 m
• T (8sec / 10rev) 0.8 sec/rev

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Example 6 determine acceleration with velocity
of 1.57 m/s

• Given m 5 kg r 20 cm 0.2 m
• T (8sec / 10rev) 0.8 sec/rev

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Example 6 determine acceleration with velocity
of 1.57 m/s

• Given m 5 kg r 20 cm 0.2 m
• T (8sec / 10rev) 0.8 sec/rev

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Example 6 determine FC with acceleration of
12,3 m/s2

• Given m 5 kg r 20 cm 0.2 m
• T (8sec / 10rev) 0.8 sec/rev

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Example 6 determine FC with acceleration of
12.3 m/s2

• Given m 5 kg r 20 cm 0.2 m
• T (8sec / 10rev) 0.8 sec/rev

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Example 7 Shelby twirls her 25g whistle on a
0.450m lanyard. She twirls the cord at a uniform
speed in a horizontal
circle. If the speed is 4.75m/sec, what is the
centripetal acceleration of the whistle? How
much tension is in the lanyard?
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Example 7 Shelby twirls her 25g whistle on a
0.450m lanyard. She twirls the cord at a uniform
speed in a horizontal
circle. If the speed is 4.75m/sec, what is the
centripetal acceleration of the whistle? How
much tension is in the lanyard?

• a 50.1 m/s2

• F 1.25 N

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Concept questions

• An object moves in uniform horizontal circular
  motion. If the radius of the object triples, what
  happens to the speed of the object?
• The speed will triple
• How does doubling velocity affect the ac?
• It increases four fold
• How would calculating Fc change if the uniform
  circular motion was vertical instead of
  horizontal?