Homework: For each of the four types of relationships, find a physics equation that
demonstrates that relationship and state which
variables show that relationship
Aim: How do we analyze relationships between
variables?
Linear RelationshipTwo variables y and x are linearly related if they
can be written in the form of an equation, y = mx +b (m is the slope and b is the y-intercept- the value
of y when the line crosses the x-axis)
Non-linear relationshipsThere are a few types of non-linear
relationships that we need to know:1.Parabolic (or Quadratic)2.Hyperbolic (or Inverse)3.Inverse Squared
Parabolic (Quadratic) RelationshipsTwo variables x and y are in parabolic
relationship if they can be expressed by an equation of the form y =ax2 + bx + c
Hyperbolic (Inverse) RelationshipTwo variables x and y are in a hyperbolic
relationship if they can be expressed in the form y = a/x.
Inverse Square RelationshipTwo variables x and y are in an inverse
square relationship if they can be expressed in the form, y = a/x2
Linear or Non-linear?
Write down the equations. State whether x and y are linearly or non-linearly related. If non-linear, state what type of non-linear relationship.
1. y = 6x 2. y = 2/x 3. y = 10 + 4x2
4. x2y2 = 23 5. 3y = 2x + 7 6. 44y = 3/x2
7. y = 0.5x + z 8. y1/2 = 8x + 8 9. 15x = 20y
Application to Physics: The Centripetal ForceFc = centripetal forcer= radiusv = speed of objectm = mass of objectFc= (m v2)/rAccording to this equation, what is the
relationship between?i)Force and massii) Force and speed of objectiii) Force and radius of circular motion
Application to Physics: The Gravitational Force
Linear or Non-Linear?
a)Gravitational Force and massb) Gravitational force and radial distance between the masses
Practice calculating slope of a line
12
12
xx
yym
The slope of a line measures its steepness.
The formula we use to calculate slope is slope = rise/run
Practice Problem 1: Find the slope
This line goes through both of these points,(6,0) and (9,2)
Slope = ???
Practice Problem 2: Find the slope
Slope = ???
Practice Problem 3:Find the slope of a line that goes through
points(4,7) and (2,11)
Write the equation of this line.
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