Further mechanics (everything) (done whilse going through revision book) Flashcards
what is anglar speed
the angle at wich an object rotates per second (ω)
give anglar speed equation and units
angler speed = angle turned per second
ω = θ/t
units = radians per second
give an equation for anglar speed (sometimes called tangential velocity) related to linear speed
ω = v/r
frequency is the number of…
complete revelutions per second
time peried is…
time taken for a full revelution
show how frequenxy and peried are related to anglar speed (ω) algebraicly
ω = θ/t
θ = 2π and t = T
therefore, ω = 2π/T
also:
T = 1/f
therefore, ω = 2πf
ω = 2π/T = 2πf
why does an object that is travelling in circles constantly accelerate?
what is this called and where is this directed
because the direction the object is traveling is constently changing
therefore
the velocity ic constently changing
therefore
as acceleration is the rate of change of velocity, the object is constantly accelerating
this is called centripetal acceleration and is directed to the center of the circle (perpendicular to velocity)
give the 2 centripetal acceliration equation and the unit
a = ω^2 x r
a = (v^2)/r
unit = ms^-2
- centripetal force equations (2) and unit
- where is this directed
F = m x (V^2)/r
F = m x (ω^2)r
units = N
(its just M x the accelration equations in accordence with F = ma)
- to the center of the circle (just like acceliration)
total enegy in SHM will always = _____+ _____
Ep + EK
where Ep is the potential enegy weather its stored in gravitational potential enegy for pendulims or elastic stored enegy for springs
draw the graph of energy ever displacement with Ep and Ek in it
pg 100 revision book
at the midpoint Ep is ______ and Ek is _______
at the max displacment Ep is ______ and Ek is _______
therefore the sum of Ek and Ep stays _____
0, max
max,0
constent
the frequency and period are independent of the ________
amplitude
in SHM the acceleration ∝ ______
where acceleration is always in the _______ direction of _______
minus displacment (x)
opposit, displacement(x)
SHM acceleration equations:
a =
a(max) =
a = -ω^2 * x
a(max) = ω^2 * A
where A is max displacment
SHM velocity equations:
v =
v(max) =
v = +or- ωroot(A^2 - x^2)
v(max) = ωA
SHM dicplacment equations:
x =
for this equation to work you need to start timing at ____ ____________
x = Acos(ωt)
max displacement
what is the equation for a force pulling a spring back to the equilibrium position in SHO
why is there a minus
F = -Kx
where x is decplacment from equalibrium
(notice this is the same equastion as hooks law in meterials F=KΔL, ΔL is x and)
there is a - because we are describing the force bringing the spring back to equilibrium.
or
you can just remember that acceleration is always opposite to diplaycment
what is K when dealing with springs
spring constent (or stiffness)
(same as in meterials)
equation for peird of mass ocilationg on a spring
T = 2π root(m/k)
- the equation for the period of a pendulum and units
- this formula is only accurate for when…
- L is measured form ______ to _____ __ _____
- T = 2π root(L/g)
- small angles of ocillation are used (up to about 10 degrees)
- pivot, center of mass
what is free vibrations
this will mean a oscillating system will have the _______ _______ forever
when there is no transfer of energy to or from system
same amplitude
forced vibration happens when there is a _________ ______ ______
the frequency of this force is called ________ __________
external driving force
driving frequency
if the driving frequency is much less the the resonant frequency then the two are _______ _______, the ocilator just…
in phase
followes the motion of the driver
if the driving freqiency is much greater then the resonant frequency then the two are ____ ____ ______ as the ocilator…
out of phase
won’t be able to keep up with the driving frequency
when does reconence happen?
draw quick graph of amplitude over driving frequncy showing recence frequency
when,
driving frequency = Resonant frequency
pg104
amplitude is very ______ at reconence frequency
large
damping happens when _______ __ _____ to the seroundings
enegy is lost
dampening reduces _________
amplitude of ocilation (thereofre also enegy in the system)
draw quick graph of displacment over time for:
1. light damping
2. heavy damping
3. critical damping
4. overdamping
pg105 of revision book
damping can aslo effect _________ _____
(not A)
resonance frequency
lightly damped systems have very _______ resonance peaks
sharp
(but not as sharp or tall as the undampined systems resonent peak)
heavily damped systems have ________ resonsnce peaks
flatter
real exam question:
state the conditions for SHM (2m)
1m - The acceleration is proportional to the displacement
1m - the acceleration is in opposite direction to displacement
just remember a ∝ -x
in the pndulmum practical:
how far do you displace the pendumum when performing the practical
- less then 10 degrees (small angle)
in the pndulmum practical:
how can you ensure you meause time peried accuretly(3)?
- measure 10T and then divide by 10 (reduce percentage uncertainty)
- use a fiducial marker (to reduce parallax error)
- meausre 3 x 10T (spot anomalies)
as a system experiences more damping its peak amplitude during resonence __________, the curve on a amplitude frequency graph becomes _____ as enegy is ______.
the resonent frequency also _________ when damping occcors.
decreses, flatter, lost
decreses
What is the phase diffrence between the veriation of displacment over time and the veriation of acceleration with time for a body
pie or 180degrees
e.g
max a is -max x
and
-max a is max x
think of a∝-x
exam question:
state what is ment by simple harmonic motion (1mark)
- acceleration is preportinal to displacment
- acceleration is in the opposit direction to displacment
a∝-x
velocity is ___ out of phase from x
acceleration is ____ out of pahse with x
90
180
