Equations we need to know for solid mechanics:
Newton’s second law:
F = ma
Friction:
Limiting friction = fs
fs∝N
Dynamic friction = fd
fd∝N
Dynamic friction < static friction:
f s=μ s N
f d=μ d N
F ≤ μN
Standard acceleration for constant acceleration:
2 2
v2 = u2 + 2as ω 1 =ω0 +2 ω̇ θ
v = u + at ω 1=ω 0+ ω̇ t
1 2
s = ut + ½ at2 θ=ω0 t+ ω̇ t
2
Acceleration under variable force:
Object has thrust T and drag BV2
COME BACK TO THIS IT IS SO LONG HOLY SHIT AND SURELY THERE MUST BE AN EASIER WAY TO DO
ALL THIS STUFF
Power = force x velocity
Moment of a force:
Moment = fd (d = perpendicular distance)
If we know about some other point on line of action of force:
Moment = Fa sinα=( Fsinα ) a
Two equal and opposite forces (not in same line) form a couple
, Moment about any point is Fd
Momentum – useful when force varies with time:
For linear motion:
F = ma
t2 t2 t2 v2
dv
∫ F dt=∫ ma dt=m∫ dt dt=∫ 1 dv
t1 t1 t 1 v 1
If F = constant
F = (t1 – t2) = m(v1 – v2)
Ft = m(v-u)
For rotational motion
Momentum = Iω
Kinetic Energy:
Initial KE = ½ (m1u12 + m2u22) Final KE = ½ (m1v12 + m2v22)
1 m1 m2
Change in KE = (v 1−v 2)2
2 m1 +m2
Statically determinate stuffs:
Frame with
N nodes (joints)
M members
R reaction components
Number of unknowns = m + r
Number of equations = 2n (resolving twice at each node)
Frame is statically determinate if
2n = m + r
Statically determinate 2n = m + r
Statically indeterminate 2n < m + r
Kinematic 2n > m + r
Except in special case kinematic!!
Newton’s second law:
F = ma
Friction:
Limiting friction = fs
fs∝N
Dynamic friction = fd
fd∝N
Dynamic friction < static friction:
f s=μ s N
f d=μ d N
F ≤ μN
Standard acceleration for constant acceleration:
2 2
v2 = u2 + 2as ω 1 =ω0 +2 ω̇ θ
v = u + at ω 1=ω 0+ ω̇ t
1 2
s = ut + ½ at2 θ=ω0 t+ ω̇ t
2
Acceleration under variable force:
Object has thrust T and drag BV2
COME BACK TO THIS IT IS SO LONG HOLY SHIT AND SURELY THERE MUST BE AN EASIER WAY TO DO
ALL THIS STUFF
Power = force x velocity
Moment of a force:
Moment = fd (d = perpendicular distance)
If we know about some other point on line of action of force:
Moment = Fa sinα=( Fsinα ) a
Two equal and opposite forces (not in same line) form a couple
, Moment about any point is Fd
Momentum – useful when force varies with time:
For linear motion:
F = ma
t2 t2 t2 v2
dv
∫ F dt=∫ ma dt=m∫ dt dt=∫ 1 dv
t1 t1 t 1 v 1
If F = constant
F = (t1 – t2) = m(v1 – v2)
Ft = m(v-u)
For rotational motion
Momentum = Iω
Kinetic Energy:
Initial KE = ½ (m1u12 + m2u22) Final KE = ½ (m1v12 + m2v22)
1 m1 m2
Change in KE = (v 1−v 2)2
2 m1 +m2
Statically determinate stuffs:
Frame with
N nodes (joints)
M members
R reaction components
Number of unknowns = m + r
Number of equations = 2n (resolving twice at each node)
Frame is statically determinate if
2n = m + r
Statically determinate 2n = m + r
Statically indeterminate 2n < m + r
Kinematic 2n > m + r
Except in special case kinematic!!
