ENGR 2010 —Statics

Math Skills Course Primer

Prerequisites: MATH 1210MATH 1210, MATH 1220MATH 1220, PHYS 2210PHYS 2210

Topics covered: force and position vectors; equilibriumof particles; rigid bodies; equivalent system of forces;equilibrium; free body diagrams; static analysis oftrusses, frames, and machines; centroids and centersof gravity; friction; and moments of inertia.

Math concepts to review:

1. Vectors & Vector operations

  • cartesian vector notation
  • magnitude of vectors
  • unit vectors
  • sum of vectors
  • dot product
  • cross product
Vectors and Vector Operation

vectors are used to represent forces on a body

distributed load on beam force on beam = integral distributed load

integrals can be used to analyze distributed loads

2. Calculus

  • fundamental theorem of calculus
  • derivatives
  • indefinite integrals
  • definite integrals
  • centroid & center of mass equations

3. Trigonometry

  • trigonometry in 3-D space
  • polar coordinate system (2-D)
  • cylindrical & spherical coordinatesystems (3-D)
  • trigonometric identities
Trigonometry

trigonometry can be used to split force vectors into components

Equation: Uppercase-Sigma F = ma

Other Concepts:

  • solving systems of equationswith 2 and 3 unknowns
  • helpful: solving systems ofequations in matrix form
  • right-hand rule
right hand rule