Contents - 19
VPOTENTIAL.................................................................................................................................................................4-79
XNUM..............................................................................................................................................................................4-79
XQ....................................................................................................................................................................................4-80
ZEROS............................................................................................................................................................................4-80
? .......................................................................................................................................................................................4-81
∞.......................................................................................................................................................................................4-81
5. Equation Reference ...............................................................................................................................................................5-1
Columns and Beams (1) .....................................................................................................................................................5-3
Elastic Buckling (1, 1) ................................................................................................................................................5-4
Eccentric Columns (1, 2).............................................................................................................................................5-4
Simple Deflection (1, 3)..............................................................................................................................................5-5
Simple Slope (1, 4)......................................................................................................................................................5-5
Simple Moment (1, 5) ................................................................................................................................................. 5-6
Simple Shear (1, 6)......................................................................................................................................................5-6
Cantilever Deflection (1, 7).........................................................................................................................................5-7
Cantilever Slope (1, 8) ................................................................................................................................................ 5-7
Cantilever Moment (1, 9)............................................................................................................................................ 5-8
Cantilever Shear (1, 10) .............................................................................................................................................. 5-8
Electricity (2) .....................................................................................................................................................................5-9
Coulomb's Law (2, 1)................................................................................................................................................ 5-10
Ohm's Law and Power (2, 2)..................................................................................................................................... 5-10
Voltage Divider (2, 3) ............................................................................................................................................... 5-11
Current Divider (2, 4)................................................................................................................................................5-11
Wire Resistance (2, 5)............................................................................................................................................... 5-11
Series and Parallel R (2, 6)........................................................................................................................................5-12
Series and Parallel C (2, 7)........................................................................................................................................5-12
Series and Parallel L (2, 8)........................................................................................................................................ 5-13
Capacitive Energy (2, 9) ........................................................................................................................................... 5-13
Inductive Energy (2, 10) ...........................................................................................................................................5-13
RLC Current Delay (2, 11) .......................................................................................................................................5-14
DC Capacitor Current (2, 12).................................................................................................................................... 5-14
Capacitor Charge (2, 13)........................................................................................................................................... 5-14
DC Inductor Voltage (2, 14) .....................................................................................................................................5-14
RC Transient (2, 15).................................................................................................................................................. 5-15
RL Transient (2, 16)..................................................................................................................................................5-15
Resonant Frequency (2, 17) ...................................................................................................................................... 5-16
Plate Capacitor (2, 18) ..............................................................................................................................................5-16
Cylindrical Capacitor (2,19)......................................................................................................................................5-16
Solenoid Inductance (2, 20) ......................................................................................................................................5-17
Toroid Inductance (2, 21)..........................................................................................................................................5-17
Sinusoidal Voltage (2, 22) ........................................................................................................................................5-18
Sinusoidal Current (2, 23)......................................................................................................................................... 5-18
Fluids (3) ..........................................................................................................................................................................5-18
Pressure at Depth (3, 1).............................................................................................................................................5-19
Bernoulli Equation (3, 2) ..........................................................................................................................................5-19
Flow with Losses (3, 3).............................................................................................................................................5-20
Flow in Full Pipes (3, 4)............................................................................................................................................5-21
Forces and Energy (4) ......................................................................................................................................................5-21
Linear Mechanics (4, 1) ............................................................................................................................................ 5-22
Angular Mechanics (4, 2).......................................................................................................................................... 5-23
Centripetal Force (4, 3) ............................................................................................................................................. 5-23
Hooke's Law (4, 4)....................................................................................................................................................5-23
1D Elastic Collisions (4, 5) ....................................................................................................................................... 5-24
Drag Force (4, 6)....................................................................................................................................................... 5-24
Law of Gravitation (4, 7) .......................................................................................................................................... 5-24
Mass-Energy Relation (4, 8) .....................................................................................................................................5-24
Gases (5) ..........................................................................................................................................................................5-25
Ideal Gas Law (5, 1)..................................................................................................................................................5-25
Ideal Gas State Change (5, 2)....................................................................................................................................5-26