Student calculates $\bar{y}$ for a triangle.  Must use similar triangles get element $dA$.

Find the area, first moment of area, and coordinates of a general spandrel.  The area may be above or below the function.

Locate the centroid of a rectangle, triangle, and semi-circle on a coordinate grid.

Find the centroid of a shape made up of a rectangle and two triangles.

Find the centroid of a shape made from a rectangle, triangle, and circle.

Homework set.  Problems require finding centroid, then Moment of Inertia about a centroidal axis.

Homework set.  Use integration to find the centroid of shapes bounded by functions.

Homework set.  Use integration to find the centroid of shapes bounded by functions.

Homework set.  Find centroids of shapes by dividing them into simple subshapes.

Given a random spandrel, find the expressions for the differential elements of area and the coordinates of its centroid needed to determine the location of the centroid by integration. 

Find the centroid and the centroidal moments of inertia for a beam composed of a flat plate and two angle sections.

Calculate the centroidal moment of intertia of a rectangle with a excentric rectangular hole.

Find the centroidal moment of inertia of a sideways T shape. This requires first locating the centroid, then applying the parallel axis theorem.

This question demonstrates how to use GeoGebra applets in explore mode.

The student must construct a polygon by adding points one at a time. At any point, they can answer the question, "Is the centroid inside the polygon?"

GeoGebra's IsInRegion command is used to decide if the centroid is inside the polygon.

This question demonstrates how to construct a JSXGraph diagram using JessieCode.

The construction shows a triangle and its orthocentre, circumcentre and centroid. They are always collinear. You can move the vertices of the triangle.

Use integration to find the centroid of an area bounded by a parabola, a sloping line, and the y-axis.  

Given the moment of inertia of an area about an arbitrary axis, find the centroidal moment of inertia and the moment of inertia about a second axis.

Find centroidal moments of inertia and radius of gyration for a beam composed of  two angle sections forming a box beam.

Use a table of properties to find the Area Moment of inertia for simple shapes: rectangle, triangle, circle, semicircle, and quarter circle.

 The parallel axis theorem is not required for any of these shapes.  One situation requires subtracting a triangle from a rectangle however.

Distinguish between centroidal and non-centroidal moments of inertia.

This demonstrates how to construct a JSXGraph diagram in JME code.

The construction shows a triangle and its orthocentre, circumcentre and centroid. They are always collinear. You can move the vertices of the triangle.

Locate the centroid of a rectangle, triangle, and semi-circle on a coordinate grid.