Circular Object Lab

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Circular Object Lab
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Circular Object Lab

• Find a circular object.
• Measure the radius of the object.
• Roll the object one complete revolution. Measure
  the linear distance traveled from the start to
  the completion of one revolution.
• Enter your measurements into the chart on the
  overhead.

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Circular Object Lab - Steps

• Collect the data.

• Enter the data into the lists of the TI-83
  calculator.

• Graph the data in a Stat-Plot.

• Find a regression equation for the data.

• Write a mathematical model and explain the model.

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Step 1 Collecting Data

• Determine the units (inches, cm) to be used.

• Discuss accuracy in measurement.

• Double check or ask a partner to check your
  measurements.

• Write your measurements clearly and neatly.

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Step 2 Entering Data

• Press the Stat key on the keyboard.

• Choose Edit from the menu.

• Clear the current data from the lists.

• Use the arrow keys to place the cursor on L1.
  Press Clear followed by Enter .
  Repeat for L2.

• DO NOT press the Delete (DEL) key. It will
  delete the list.

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Step 2 Entering Data

• Enter the data into the lists.

• Press ENTER to move down the list one line.

• Use the arrow keys to move between lists or to
  edit a line.

• Make sure each list has the same number of
  entries.

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Step 3 Graph the Data

• Clear any equations in the Y function grapher.
  Press Y and clear any equations.

• Set up a Stat PlotPressChoose 1 for Stat Plot 1

• Press ENTER with the cursor on the On to turn on
  the Stat-Plot

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Step 3 Graph the Data

• Choose the scatter plot as the Type.

• Choose the appropriate list for the x and y-axis.

• When large amounts of data are displayed, use the
  . as the Mark. The square or plus may be used
  when smaller amounts a data are graphed.

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Step 3 Graph the Data

• Press Zoom-9 or ZoomStat to graph the data.

• The grapher will fit window to the data and
  display the graph.

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Step 4 Find an Equation

• Press the STAT key and arrow to CALC.

• Choose the appropriate equation type. Since the
  data is linear, choose option 4.

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Step 4 Find an Equation

• The calculator will return to the home screen.

• Enter the x-list, y-list, and y location to
  store the equation. Press L1 (2nd 1), L2 (2nd 2)
  to enter the x and y lists. Each item should be
  separated by a comma.

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Step 4 Find an Equation

• To store the equation, press the VARS key and
  arrow to Y-VARS.

• Choose Function and select one of the Y
  locations to store the equation.

• The home screen should now be similar to

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Step 4 Find an Equation

• The home screen will display the regression
  equation.

• Press Graph to see the model graphed with the
  StatPlot.

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Step 5 Write a Math Model

• The math model should always use meaningful
  variables and in most cases contain variables.
  The slope for this model is a bit tricky since
  the units of x and y are the same.

• What do x and y represent?

• x is the radius.

• y is the linear distance traveled by the object.

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Step 5 Write a Math Model

• Write a model with variables and variable units.

s(cm) 6.03r(cm) 0.76

• What are the units of the slope and y-intercept?

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Step 5 Write a Math Model

• The y-intercept would be at the point (0, 0.76).
  The units of the y-value would be cm.

• The slope would be the change in y divided by the
  change in x.

• The units divide out leaving no units for the
  slope. The slope is a ratio.

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Step 5 Write a Math Model

• In precalculus, this would lead to a discussion
  of radians in developing 2p radians as the angle
  for one complete revolution.

• The model iss(cm)6.03(radians)r(cm) 0.76(cm)

• For each 1 cm increase in the radius, the linear
  distance traveled will increase by 6.03 cm.

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Step 6 Meaning of Model

• Since we have an accepted equation for this
  activity (C 2pr), we can calculate the error
  in the lab.

• We would expect the y-intercept to be 0. An
  object with 0 radius would roll 0 units of
  distance. Find the error by dividing the
  y-intercept by the largest y-value of the data
  set.

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Step 6 Meaning of Model

• The slope is expected to be 2p. The error is
  calculated by using the formula(Expected
  Calculated)/(Expected)

• In our case (2p-6.03)/(2p) 0.04 or 4 error.