Physics 2211, Spring 2002

1
Physics 2211 Lecture 6Todays Agenda

• Reference frames and relative motion

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Inertial Reference Frames

• A Reference Frame is the place from which you
  measure.
• -- its where you nail down your (x,y,z) axes!
• An Inertial Reference Frame (IRF) is one that is
  not accelerating.
• We will consider only IRFs in this course.
• Valid IRFs can have fixed velocities with respect
  to each other.
• More about this later when we discuss forces.
• For now, just remember that we can make
  measurements from different vantage points.

3
Newtons Principle of Relativity

• Principle of Relativity (from Newton in 1600s)
• The motion of bodies included in a given space
  are the same among themselves whether that space
  is at rest or moves uniformly forward in a
  straight line.

• Newtons Principle of Relativity Restated
• The laws of mechanics (Newtons Laws) are
  invariant (the same) in all inertial
  (non-accelerating) reference frames(IRFs).
• OR
• Absolute uniform motion (or absolute rest)
  cannot be detected.

• Impact Experiments (e.g., dropping a ball,
  period of a pendulum, two objects colliding) in a
  boxcar moving with constant velocity will have
  the same results as the same experiments in a
  boxcar at rest.

4
Example(relative motion)

• Kim is sitting on a train moving at 20 m/s. She
  is throwing a ball straight up and is catching it
  at the same place she threw it. The ball is in
  the air 1.5 s. Joe is standing on the ground by
  the railroad tracks and watches Kim as she throws
  the ball.
• What is the initial speed of the ball and how
  high does it go
• as seen by Kim?
• as seen by Joe?

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Example

• The ball moves vertically in the IRF attached to
  the train (Kims IRF)

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Example

• But suppose the train is moving to the right in
  the IRF attached to the ground (Joes IRF).

• From the grounds IRF, the balls motion exhibits
  projectile motion.

Galilean velocity transformation
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Example

• The initial velocity as see my Joe is

• Magnitude of initial velocity (initial speed)

• Angle above the horizontal

8
Example

• Recall x and y components of motion are
  independent

• Therefore, vertical (y) motion is the same both
  in both IRFs

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Example

• You are swimming across a 50m wide river in which
  the current moves at 1 m/s with respect to the
  shore. Your swimming speed is 2 m/s with respect
  to the water. You swim across in such a way that
  your path is a straight perpendicular line across
  the river.
• How many seconds does it take you to get across
  ?(a) (b)(c)

50 m
2 m/s
10
Example

• The time taken to swim straight across is
  (distance across) / (vy )

• Since you swim straight across, you must be
  tilted in the water so thatyour x component of
  velocity with respect to the water exactly
  cancels the velocity of the water in the x
  direction

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Example
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Example(relative motion)

• What is the boats velocity with respect to the
  shore if
• the boat travels from point A to point B directly
  across?
• the boat crosses in the shortest possible time?

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Example

• Apply Galilean Transformation

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Example
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Example

• What is the boats velocity with respect to the
  shore if the boat crosses in the shortest
  possible time?

• Time to cross the river is given by the distance
  travel (as measured on the shore) divided by the
  speed of the boat (as measured on the shore)

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Example
17
Example
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Recap for today

• Reference frames and relative motion

• For next time Review Chapter 3 in Tipler.
  Begin Chapter 4.