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

Homework set.  Application of Parallel Axis Theorem to find area Moment of Inertia

Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.

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

Find moment of inertia of a shape which requires the use of the parallel axis theorem for a semicircle.

Find moment of inertia of a composite shape consisting of a rectangle and two triangles with respect to the x-axis. Shapes rest on the x-axis so the parallel axis theorem is not required.

Calculate the moment of inertia of a composite shape consiting of two rectangles about the x or y-axis.  Parallel axis theorem is often required.

Find the moment of inertia of semi and quarter circles using the parallel axis theorem.

Use the parallel axis theorem to find the area moment of inertia of a triangle and a rectangle about various axes.

Write expressions for the moment of inertia of simple shapes about various axes.

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.

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

Use Matlab (or Python) to fit a cubic polynomial to data, and determine where the x-axis is crossed.

Drag points on a graph to the given Cartesian coordinates. There are points in each of the four quadrants and on each axis.

Students enter equation and turning point

Students enter equation and turning point

Find the area under a curve. The step is given.

Find the area under a porabola.

Given that the circle touches the x-axis at a given point and given a point on the circumference, find the equation of the circle.

Find the gradient and y-axis intercept of a line through 2 points. The line is not vertical.

Identify the gradient and y-axis intercept of a random non-vertical line.

Drag points on an axis to plot a linear graph (integer gradient and intercept only)

Student is given two points defined symbolically, and must find the equation of the line they define, then use integration to find an equation for the area under the line, bounded by the x-axis and vertical lines through the two points.   

Calculating the angle between a vector and the positive $x$-axis.

Drag points on a graph to the given Cartesian coordinates. There are points in each of the four quadrants and on each axis.

Two quadratic graphs are sketched with some area beneath them shaded. Question is to determine the area of shaded regions using integration. The first graph's area is all above the $x$-axis. The second graph has some area above and some below the $x$-axis.

Students are asked to move an x-axis slider representing standard deviation on a normal distribution to make the area between (mean - slider value) and (mean + slider value) equal to a certain percentage. The 3 possible percentages correspond to the mean plus or minus 1, 2 or 3 standard deviations.

Students are asked to move an x-axis slider on a normal distribution to make the area to the left of the slider equal to a certain percentage. The 6 possible percentages correspond to the mean plus or minus 1, 2 or 3 standard deviations.

Given the original formula the student enters the transformed formula

Ready to use

Drag points on an axis to plot a linear graph (integer gradient and intercept only)