TWO DIMENSIONAL AND VARIED MOTION

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TWO DIMENSIONAL AND VARIED MOTION

• Projectile Motion
• The Pendulum

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Projectile Motion

• A projectile is an object that is thrown into the
  air.
• A projectile moves forward due to its inertia.
• It accelerates downward due to gravity.
• The path a projectile makes while in the air is a
  curve called a trajectory.

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Horizontal Motion

• Roll a ball along a horizontal surface, and its
  velocity is constant because no component of
  gravity acts horizontally. There is no
  acceleration.

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Vertical Motion

• Drop the ball, and it
• accelerates downward
• and covers greater
• vertical distances
• each second. It accelerates
• at 9.8 m/s2.

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Projectile Motion (see example)

• The horizontal component of motion for a
  projectile is completely independent of the
  vertical component of motion. The combination of
  both motions produce the curved path.

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Velocity of a Projectile at Various Points
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Projectile Fired at a Steeper Angle
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Paths of Projectiles Launched at Different Angles
-No Air Resistance
75?
60?
45?
HEIGHT
30?
15?
RANGE
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With No Air Resistance.

• 1. The time for a projectile to reach its
  maximum height equals the time to fall from
  that height to the ground.
• 2. The projectile is traveling at the same speed
  when it returns to the ground as it had when it
  was released.
• 3. The vertical velocity of a projectile will be
  zero at the top of its arc.

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Satellite

• A projectile that is moving fast enough that its
  arc matches the curvature of the earth.

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The Pendulum

• An object that is suspended so that it can swing
  back and forth about an axis is called a
  pendulum.
• The swing of a pendulum is an example of simple
  harmonic motion, which means it repeats itself
  over and over.

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The Pendulum

• The time of a back-and-forth swing of a pendulum
  is called the period of a pendulum. It is
  measured in seconds.
• The period of a pendulum only depends on the
  length of the pendulum and the acceleration of
  gravity. (see example)

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Calculating the period of a pendulum

• Use the equation
• Where
• T period of pendulum
• l length of pendulum
• g gravity

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Calculating the period of a pendulum

• An astronaut sets up a pendulum on the moon,
  where gravity is 1.6 m/s2. If the pendulum is 1
  meter long, what will the period of the pendulum
  be?

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