Mohr’s Circle for Mom. of Inertia
Class Today
• Print notes and examples
• Mohr’s Circle for Moments of Inertia
– Defined
– Finding max and min values
– Finding angle of rotation
• When all possible
moments and products of
inertia for a shape are
plotted on a graph, the
resulting graph is a circle.
• This graph makes it easy
to find any moment or
product of inertia for a
shape that we want. All
we have to do is use the
geometrical properties of
a circle.
• Example Problems
• Group Work Time
Mohr’s Circle for Mom. of Inertia
• Ix and Iy are plotted on
horizontal axis
• Ixy is plotted on vertical axis
• Plot point ‘X’ 1st (Ix , Ixy)
• ‘Y’ will be on opposite side
as (Iy ,-Ixy) (note signs of Ixy)
• Now you have two points
• Draw the circle through
these points
• Find any other points you
need (usually Imin and Imax)
Finding Imin and Imax
• Once the circle is drawn (see
previous slide) locate the center
point (shown here as O)
• Form a right triangle by
dropping a vertical line from
point X to horizontal axis.
• Use this triangle to find the
radius of the circle
(hypotenuse) and the angle
shown as 2θ
• Imin and Imax are simply the
center plus or minus the
Finding Theta
• It can be important to know the orientation (with respect to the x-y axis
system) of a physical object for a given moment of inertia.
• Rotating the object’s coordinate system through any angle θ will
correspond to an angle of 2θ on Mohr’s Circle.
• Theta (θ) is always measured:
– the same rotational direction on both the object and the graph.
– from point X on the graph and from the x-axis on the object.
27_Mohr's Circle