Periodic Motion

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Periodic Motion

• Chapter 7

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What does it mean when something is periodic?

• When something repeats in a pattern
• Examples?
• Seasons, days of the weeks, class schedule, the
  earth orbiting the sun

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What would happen if we increased the speed of
the cannonball?
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What if the amount the ball dropped matched the
curve of the earth?
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Is a satellite orbiting the earth at a constant
speed being accelerated?

• YES because it is changing directions

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What causes the acceleration?

• Gravity

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What is the acceleration direction?
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What about a car going around a curve
What direction would the car need to be pushed to
go around the curve
Velocity direction
Towards the right
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When the road is icy, there is not enough
friction to accelerate the car inward
Where the car goes when there is not enough
friction
Velocity direction
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Is there a force in this picture

• Forces that present include
• Gravity
• Inertia
• Force of the car on the track
• Force of the track on the car
• All these forces make up the force which cause
  the motion of the car around the loop

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Forces in a rollercoaster
The acceleration force is in the direction you
would go if the track was not there at that point
(caused by inertia)
Fc
Fc
Fc
The track provides an acceleration/force that
makes the car go in a circular path
Fc
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If we only looked at the forces that are only
acting on the car, how would they compare in the
locations below
Force of track
There needs to be more force going up to change
the cars motion
gravity
There needs to be more force going down so the
car does not come off of the track (goes down)
Force of track
gravity
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Compare the forces acting on the car for each of
the locations below
The net force at each point is towards the center
of the circle
gravity
gravity
gravity
Force of track
gravity
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Centripetal Acceleration

• Causes an object to travel in a curved or
  circular path
• Acceleration is towards the centerof the
  circular path
• ac v2 r

4 p2 r
t2
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Who moves faster on a merry go round?

• Show where v 2 p r

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Example problem 1

• A runner goes around a curve with a radius of 25
  m at 8.8 m/s
• What is her acceleration?
• If she has a mass of 70 kg, what force do her
  shoes provide to keep her on the track?

3.10 m/s2
217 n
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Example problem 2

• A 30.0 kilogram little girl rides a
  merry-go-round that is spinning at a rate of 8.00
  revolutions per minute.
• What is the time for one revolution?
• b) What is the magnitude of the acceleration that
  is keeping the girl going in the circle, if the
  merry-go-round has a radius of 2.25 meters?

7.5 s
1.57 m/s2
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Homework

• Page 152
• RC (4,7,8)
• Problems (13,15,19)

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Remember periodic is

• When something repeats in a pattern
• Examples
• Seasons, days of the weeks, class schedule, the
  earth orbiting the sun

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Another type

• Simple Harmonic Motion
• Periodic because it repeats
• Must have a restoring force that pushes the
  object back to the equilibrium position
• Remember equilibrium means zero net force

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Pendulums (from DYO lab)

• Formula for a pendulum period
• T 2p l

g
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What is a restoring force?
Force caused by weight can be broken into parts
Equilibrium positionNo Restoring force
Swing Direction
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Whiteboard spring example
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Mass on a spring Restoring force?-Equilibrium
Position?
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Home Work
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Pendulums (investigate as a class)

• What does the mass on a period?
• Mass had no effect
• What effect would the angle have on the period?
• Angle of release had no effect
• What effect does the length have?
• As length increased, so does the period