Rotational engineering Flashcards
inertia
a measure of how an object resist a change in velocity
larger the inertia, the larger the force applied is needed to be able to change its velocity
moment of inertia
measure of how difficult it is to rotate an object or to change its rotational speed
measures resistance to rotation and depends on mass and distance from axis of rotation
equation for moments of inertia
I =mr^2
moments of inertia
distribution of mass
a hollow object will have a larger moment of inertia to a solid one
e.g. a flywheel has a larger moment of inertia to a wheelbarrow of a similar mass and its more distributed
rotational kinetic energy
depends on moment of inertia
Ek = 0.5 I w^2
moment of inertia for a solid object
0.5mr^2
angular displacement
the angle trough which a point has been rotated
angular velocity
a vector quantity
describes the angle a point rotates through per second
w = △θ / △t
angular speed
scalar
magnitude of angular velocity
angular acceleration
the rate of change of angular velocity
α =△w / △t
torque
when a force or couple causes an object to turn
the turning effect is known as torque
couple
a pair of forces which cause no resultant linear motion
equationS for torque
T = Fr
T = Iα
work done and toque
when you rotate an object work is done to make it move
W = Tθ
power and torque
power is work done in a given time
P = Tw
w = angular velocity
frictional torque
machines with rotating parts will experience an oppsing frictional torque
some of the power of the machine is used to overcome this torque
net torque
Tnet = T applied - T frictional
flywheel
a heavy wheel with a high moment of inertia in order to resist a changes to its rotational motion`
how a flywheels works
flywheels are ‘charged’ when spun turning input torque into rotational kinetic energy
as long as flywheels keeps spinning at this rate it stores energy for later use
flywheels and frictional torque
just enough power is continuously put in to overcome frictional torque, keeping flywheels fully charged
when extra energy is needed in other parts of the machine, the flywheel decelerates transferring some of its Ke to other parts of the machine
flywheel batteries
flywheels designed to store as much energy as possible
factors which effect energy stored
- increase in mass (moment of inertia) hence Ke ∝ m
-increase in angular speed - energy stored increases with angular speed squared
-wheel with spokes - mass more concentrated further away from axis of rotation (I)
limits on energy capacity
- a gaint heavy wheel, taking too much space is impractical
-too much angular speed can break the flywheel apart due to centrifugal force
what are modern flywheel made of
carbon fibre to allow higher speeds without disintegrating although it is lighter than steel
how does flywheels lose some of its energy
flywheels still loses some energy to air resistance and friction between wheel and bearings on which it spinsh
how to combat energy loss in flywheel
-lubricate it to reduce friction
-leviated with superconducting magnets so there is no contact between bearings and wheel
-operate in vacuums or sealed cylindersto reduce drag from air resiatnce
load torque
torque due to resistive forcesthat a machine must oppose to be useful
uses of flywheels
used in machines to balance or smooth the engine torque and the load torque
use of flywheels in systems with a power source that varies
if an engine kicks in intermittently, a flywheel can be used to keep the the angular velocity of any rotating component constant
the flywheels uses each spurt of power to charge up
it then delivers energy it stored smoothly to rest of the system, instead of bursts
if engine torque is higher than load torque
the flywheel will charge up by accelerating so the spare energy is stored until its needed
flywheel applications
-vehucles
-machines in production process
-potter wheel
-regenerative braking
-power grids
-wind turbines
regenerative braking
in some electric cars when the brakes are applied the flywheel is engaged
the flywheel then charges up with energy that would otherwise be lost
when when the vehicle is ready to accelerate, the flywheel uses its energy turn the vehicles wheel faster before being disengaged until needed again
potters wheel
powered by a foot pedal, meaning its hard to apply a constant force
flywheel used to keep the speed of the wheel constant
power grid
when lots of electricity is used in an area, the grid sometimes cannot meet that demand
flywheels can be used to store surplus power in times of low demand adn provide extra power when backup power stations are started up in times of high demand
wind turbines
flywheels are used to store excess power on windy days or during off-peak times to provide power n days with no wind
advantages of flywheels
-very efficient
-lasts a long time without disintegrating
-recharge time is short
-they can react and discharge very quickly
-environmentally friendly (dont rely on chemicals)
disadvantages of flywheels
-much larger and heavier than other storage methods (batteries)
-safety risks, can beeak apart at high speeds. protective casing to protect against this can make it heavier
-energy can be lost through friction
-if used in moving objects, they can oppsoe changes in direction, which can cause problems for vehicles
angular momentum
I w
conserbation of angular momentum
always conserved, when no external forces are applied angular momentum is constant
I initial x w initial = I final x w final
angular momentum
ice skater spinning example
at the start of the spin her arms are away from the body
when arms are pulled closer, she begins to spin faster due to conservation of angular momentum
as she pulls in her arms she decreases her moment of inertia so her angular velocity muct incrase in order to conserve momentum
angular impulse
change in angular momentum
angular impulse = △(lw)
equation f0r angular impulse IF torque on the system remains cosntant
△(Iα) = T△t
How to calculate Ep lost
Ek of pulley + Ek mass
