Math General Flashcards
(36 cards)
Mechanics Modelling assumptions
Smooth pulley
Light pulley
Inextensible string
Particle
Rod
Smooth / Rough surface
Mechanics Modelling assumptions- Smooth pulley
Tension on either side of the pulley is equal
Mechanics Modelling assumptions - light string
Tension is equal throughout the string
Mechanics Modelling assumptions - inextensible string
Both particles have the same acceleration
Mechanics Modelling assumptions - particle
Ignore air resistance, Ignore rotational effects
Mechanics Modelling assumptions - Rod
Means that it is rigid (doesn’t bend) and has no thickness
CP1 - 9 - converting vector to Cartesian equation of a plane
Dot each direction vector in plane with xyz = 0 to form 2 simultaneous equations and let a=1 and solve them for normal vector xyz
CP1 - 9 - Finding angle between 2 lines
Use dot product on the direction of each of the lines
CP1 - 9 - Finding angle between line and plane
Use dot product on the direction of the line and the normal to the plane. Subtract the angle found from 90.
CP1 - 9 - Finding angle between 2 planes
Use dot product on the direction of the normals of each of the planes
CP1 - 9 - Finding POI between 2 lines
Set the general point on both line equal to a point (x,y,z) and solve for lambda and mu and for x,y,z to find POI
CP1 - 9 - Finding POI between line and plane
Sub in general point on line into Cartesian equation of plane and find value of mu and poi.
CP1 - 9 - Finding POI between 2 planes
Find 2 common points on both planes and find the vector through them and form line equation.
CP1 - 9 - Finding shortest distance between 2 skew lines
Find general point on L1 & L2
Find vector between them
Ensure this is perp to L1 & L2
CP1 - 9 - Finding shortest distance between 2 parallel lines
Find general point on L1 & L2
Find vector between them - use t = mu - lambda
Ensure this is perp to L1
CP1 - 9 - Finding shortest distance between a point and a plane
CP1 - 9 - reflecting a point in a plane
Find equation of line through point and closest point on the plane using coordinates of point and Normal to plane.
Put general line eqn in plane eqn to find value for lambda. Double value of lambda and sub into line eqn to find reflected point.
CP1 - 9 - reflecting a line in a plane
Find POI
Reflect a point on the line in the plane
Find the eqn of the line through these 2 points
Inverse of 2x2 matrix
Determinant and inverse of a 3x3 matrix
Planes meeting at single point
Sheaf
Prism
After eliminating variables the 2 equations are inconsistent
Ax+by=c
Ax+by=d
Parallel and non identical planes
