Rotational Kinematics/Dynamics and Fluids Flashcards
Formula for Angular velocity
ω = (θf - θi) / t
Formula for Angular acceleration
α = ω/t
How is angular velocity affected by the position of the object
The angular velocity remains the same independently of the objects position
How is translational velocity affected by the position of the object
The farther you are from the center the more translational velocity you have
I rev is equal to
2π
Center of mass formula
Xcm = (m1x1 + m2x2 +…./m1+m2+…)
Formula for torque
τ = F*l (perpendicular force x lever arm) or τ = Iα (inertia x angular acceleration)
When approaching torque problems, which force do you use
Only use the perpendicular force
Formula for Inertia
I = (mr^2)
Mass distributed towards the outside
Has more intertia
Mass distributed towards the inside
Has less inertia, will reach bottom first (solid)
Formula for Angular Momentum
L =Iω
Formula for Rotational KE
KE = 1/2(Iω^2)
What are the values of force and torque during static equillbirum
F=0
τ = 0
How does the gravity of an object relate to the specific gravity of H2O
If an object has 2x the gravity of H2O, then its specific gravity is 2.
If its gravity is 1/2 of H2O then the SG is 1/2 etc.
Formula for pressure
P = F/A
Units for pressure
1atm = 760 torr = 760mmHg = 100,000Pa
Formula for Hydrostatic Pressure
p = ρ(fluid) x g x h(depth)
Every 10m depth in H2O equals
1 atm pressure
Air can be looked at as a fluid in that
The deeper you go the more the pressure increases
When the liquid levels are equal
The pressure inside will equal the pressure in the external environment
Formula for Buoyancy Force
Fb = ρgV Fb = buoyant force of a liquid acting on an object ρ = density of the liquid g = gravitational acceleration V = volume of liquid displaced
If the object is floating the buoyancy force will equal
The objects weight
Formula for % submerged
(Density of object / density of fluid) x 100
The difference in height between the fluid is equal to the
Difference between the pressures
Formula for Specific Gravity
SG = (density of substance)/(density of H2O)
Density of water
1000 kg/m^3
In an enclosed structure, fluid force is the same everywhere. This gives rise to the formula
A1d1 = A2d2
Formula for a Hydraulic Jack
(F1/A1) / (F2/A2)
Laminar Flow
Straight line flow of lines that don’t interact. Once the speed picks up you reach a point of change into turbulent flow where uniformity breaks down.
Turbulent flow
Usually we aim to avoid this kind of flow since it lacks uniformity.
Flow rate formula
A1v1 = A2v2
Within a system the flow rate is always
Constant
Bernoulli’s equation
P1+1/2ρv1^2+ρgh1=P2+1/2ρv2^2+ρgh2
