Mathematical Models in Mechanics

Assumptions and approximations often used to simplify the mathematics
involved:

a) a rigid body is a particle,

b) no air resistance,

c) no wind,

d) force due to gravity remains constant,

e) light pulleys and light strings etc. have no mass,

f) the tension in a light string which remains taut will be constant throughout its length.

g) if a pulley is light or smooth the tensions in the a string going round the pulley will be

equal on both sides; the same is true for a smooth peg,

h) if a string is inextensible and remains taut, the accelerations of two particles, one fixed at

each end, will be equal,

i) if a rod is uniform  constant mass per unit length  the centre of mass will be in the

middle,

j) a lamina is a uniform flat object of negligible thickness,

k) the earth’s surface, although spherical, is usually modelled by a plane,

l) surface is smooth - no friction,

m) forces behave like vectors.