In the following exercises, consider a lamina occupying the region R and having the density function \(\rho\) given in the first two groups of Exercises.

a. Find the moments of inertia \(I_{x}\), \(I_{y}\), and \(I_{0}\) about the x-axis, y-axis, and origin, respectively.

b. Find the radii of gyration with respect to the x-axis, y-axis, and origin, respectively.

R is the triangular region with vertices (0, 0), (1, 1), and (0, 5); \(\rho(x, y)=x+y\).

Text Transcription:

rho

I_x

I_y

I_0

rho(x, y)=x+y

Week 8 Study Guide Gestalt View - Insight in Problem Solving: 2 ways to solve problems: o Analysis “Reproductive Thinking”- based on the old o Insight Aha! Experience Productive thinking – moves beyond what you know to something new Leaps of insight Current question in Gestalt psychology: are there different mechanisms in solving a problem through insight vs. analysis o Components of Insightful Solutions 3 criteria: Impasse restructuring of problem Aha! Moment + Subjective feeling of certainty Distant and unprecedented connections (remote analogies) Unconscious processes “Relaxation” of the brain (don’t occur when actively trying to solve problem) o Methods for fostering random connections i.e. ping pong tables in writing room Attempt to induce Aha!