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Use units to prove that equations are invalid
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Speed - measured in meters per second (m / s)
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A dimensionally consistent equation naturally takes the same form in all possible systems of units
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Consistent
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Inconsistent
Scientific notation & metric multipliers
Be able to:
• Write numbers in scientific notation
• Write SI units in the correct format
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Denominator units are written in the numerator with negative exponents
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g
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5 m / s2 is written 1
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A digital measuring device, on the other hand, is only “good” to the
least significant digit’s place
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Orders of magnitude
A number rounded to the nearest power of 10 is called an order of
magnitude
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• 10 50 kilograms / 10 -30 kilograms = 10 80
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• The answer is 80 orders of magnitude
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2 – Uncertainties and errors
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Random and systematic errors
Random error is error due to the recorder, rather than the instrument used for the measurement
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• Different people may measure the same line slightly differently
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• A voltmeter might have a zero offset error
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The precision of a measurement is how close a number of measurements of the same quantity agree
with each other
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It may usually be determined by repeating
the measurements
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The accuracy of measurements is often reduced by systematic errors, which are difficult to
detect even for experienced research workers
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Fractional error is given by
Percentage error is given by
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Be able to:
• Know the difference between absolute, fractional and percentage uncertainties
• Calculate these uncertainties
Propagating uncertainties through calculations
Be able to:
• Find the uncertainty in a sum or difference
• Find the uncertainty in a product or quotient
• Find the uncertainty of any equation
(Add percentage uncertainties)
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Uncertainty of gradient and intercepts
Be able to:
• Look for and draw lines of best fit
Look for the line to lie within all horizontal and vertical error bars
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3 - Vectors and scalars
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Vectors and scalar quantities
• A vector quantity is one which has a magnitude (size) and a spatial direction
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Examples of scalar quantities
Speed, Distance, Time, and Mass
Examples of vector quantities
Velocity, displacement, force, weight and acceleration
• A vector can be in any direction
• Signs can be used to signify what direction the vector is in
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Be able to:
• Distinguish between vector and scalar quantities
• Identify vector and scalar quantities
Combination and resolution of vectors
• Vectors have a tip and a tail
Be able to:
• Find the sum of two vectors
• Multiply and divide vectors by a scalar
• Resolve a vector (break down into x component and y component)
To find the sum of two vectors:
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Draw a line from the first vector's tail to the second vector's tip
If its subtracting a vector, reverse the vector's direction
To multiply a vector by a scalar, increase its length in proportion to the scalar multiplier
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