General

Question 1

Determinant

Answer 1

A weird way of calculating a cross product. Multiply by the first coefficient, then cross out that row and column as a new matrix/discriminant. That portion is minus the previous.

Ex: -1i + 1j -2K Cross 2i -3j +4j = disc (1, -2 over -3, 4) i - disc(1, -2 over 2, 4) + (-1, 1 over 2, -3)k = [(14)-(-2-3)]i - [(-14)-(-22)]k + [(-1-3)-(12)]k = -2i + k.

Question 2

Force of Gravity on incline

Answer 2

Fg parallel = mg sin theta, Fg perp = mg cos theta

Question 3

Work Kinetic Energy Theorem

Answer 3

Net Work = Change in KE, often as a middleman to other forms of energy

Question 4

Frictional Work to Energy

Answer 4

Work by Friction (or non con) = change in ME when in a isolated system.

Question 5

Conservation of Mechanical Energy

Answer 5

MEf = MEi when in a isolated system & with no non-con forces

Question 6

Conservative Force to Work

Answer 6

Conservative Force = neg derivative of PE associated with respect to position.

Question 7

Conservation of Momentum

Answer 7

PEi = PEf, only when all forces internal. Derive from Fext =0, so derivative of momentum with respect to time is 0. (F=ma = dp/dt). Collisions & Explosions!

Question 8

Deriving Impulse

Answer 8

F = dp/dt or F dt = dp. Take integral with respect to time and momentum, for change in momentum = time integral of F. Another vector! Ns.

Distinct from Work, which is based in position.

Question 9

Impulse Approximation

Answer 9

Fnet is approximately Fimpact, when forces are large over short time. Often considered to be constant for finding impulse.

Question 10

Collision Elasticity

Answer 10

Momentum is conserved regarldless, but inelastic collisions don’t conserve kinetic energy. Perfectly inelastic collisions stick objects together - maximum loss of kinetic energy.

Question 11

Center of Mass

Answer 11

= Sum of mass * location of each particle, divided by sum of system mass.

Question 12

Velocity/Acceleration of CM.

Answer 12

Time derivative of position. Mass constant, bt becomes sum of mass * velocity over sum of mass. Same for acceleration.

Question 13

Center of Mass Position for rigid object with shape

Answer 13

rcm = integral of position with respect to mass over total mass (outside integral)

r is just a position vector for 3D space, like x.

Question 14

Volumetric Mass Density

Answer 14

rho = mass over volume (kg/m^3)

Question 15

Surface Mass Density

Answer 15

sigma = mass over surface or area (kg/m^2)

Question 16

Linear Mass Density

Answer 16

lamda = mass over length (kg/m)

Question 17

Cross Product

Answer 17

Measure of the area formed between two vectors. Magnitude equal A*B sin theta, with direction determined by right hand rule. Use discriminant for unit vector direction calculation, and pythagorize for magnitude.

Torque is a cross product, as is angular momentum.

Question 18

Dot Product

Answer 18

Measure of perpendicularity in vectors. Magnitude equals AB cos theta. No direction - scalar.

Work is a dot product.