Further mechanics (everything) (done whilse going through revision book)

Question 1

what is anglar speed

Answer 1

the angle at wich an object rotates per second (ω)

Question 2

give anglar speed equation and units

Answer 2

angler speed = angle turned per second

ω = θ/t

units = radians per second

Question 3

give an equation for anglar speed (sometimes called tangential velocity) related to linear speed

Answer 3

ω = v/r

Question 4

frequency is the number of…

Answer 4

complete revelutions per second

Question 5

time peried is…

Answer 5

time taken for a full revelution

Question 6

show how frequenxy and peried are related to anglar speed (ω) algebraicly

Answer 6

ω = θ/t
θ = 2π and t = T
therefore, ω = 2π/T
also:
T = 1/f
therefore, ω = 2πf

ω = 2π/T = 2πf

Question 7

why does an object that is travelling in circles constantly accelerate?

what is this called and where is this directed

Answer 7

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)

Question 8

give the 2 centripetal acceliration equation and the unit

Answer 8

a = ω^2 x r

a = (v^2)/r

unit = ms^-2

Question 9

1. centripetal force equations (2) and unit
2. where is this directed

Answer 9

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)

2. to the center of the circle (just like acceliration)

Question 10

total enegy in SHM will always = _____+ _____

Answer 10

Ep + EK
where Ep is the potential enegy weather its stored in gravitational potential enegy for pendulims or elastic stored enegy for springs

Question 11

draw the graph of energy ever displacement with Ep and Ek in it

Answer 11

pg 100 revision book

Question 12

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 _____

Answer 12

0, max

max,0

constent

Question 13

the frequency and period are independent of the ________

Answer 13

amplitude

Question 14

in SHM the acceleration ∝ ______

where acceleration is always in the _______ direction of _______

Answer 14

minus displacment (x)

opposit, displacement(x)

Question 15

SHM acceleration equations:
a =
a(max) =

Answer 15

a = -ω^2 * x
a(max) = ω^2 * A
where A is max displacment

Question 16

SHM velocity equations:
v =
v(max) =

Answer 16

v = +or- ωroot(A^2 - x^2)
v(max) = ωA

Question 17

SHM dicplacment equations:
x =
for this equation to work you need to start timing at ____ ____________

Answer 17

x = Acos(ωt)

max displacement

Question 18

what is the equation for a force pulling a spring back to the equilibrium position in SHO

why is there a minus

Answer 18

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

Question 19

what is K when dealing with springs

Answer 19

spring constent (or stiffness)

(same as in meterials)

Question 20

equation for peird of mass ocilationg on a spring

Answer 20

T = 2π root(m/k)

Question 21

1. the equation for the period of a pendulum and units
2. this formula is only accurate for when…
3. L is measured form ______ to _____ __ _____

Answer 21

1. T = 2π root(L/g)
2. small angles of ocillation are used (up to about 10 degrees)
3. pivot, center of mass

Question 22

what is free vibrations

this will mean a oscillating system will have the _______ _______ forever

Answer 22

when there is no transfer of energy to or from system

same amplitude

Question 23

forced vibration happens when there is a _________ ______ ______

the frequency of this force is called ________ __________

Answer 23

external driving force

driving frequency

Question 24

if the driving frequency is much less the the resonant frequency then the two are _______ _______, the ocilator just…

Answer 24

in phase

followes the motion of the driver

Question 25

if the driving freqiency is much greater then the resonant frequency then the two are ____ ____ ______ as the ocilator…

Answer 25

out of phase

won’t be able to keep up with the driving frequency

Question 26

when does reconence happen?

draw quick graph of amplitude over driving frequncy showing recence frequency

Answer 26

when,
driving frequency = Resonant frequency

pg104

Question 27

amplitude is very ______ at reconence frequency

Answer 27

large

Question 28

damping happens when _______ __ _____ to the seroundings

Answer 28

enegy is lost

Question 29

dampening reduces _________

Answer 29

amplitude of ocilation (thereofre also enegy in the system)

Question 30

draw quick graph of displacment over time for:
1. light damping
2. heavy damping
3. critical damping
4. overdamping

Answer 30

pg105 of revision book

Question 31

damping can aslo effect _________ _____

(not A)

Answer 31

resonance frequency

Question 32

lightly damped systems have very _______ resonance peaks

Answer 32

sharp
(but not as sharp or tall as the undampined systems resonent peak)

Question 33

heavily damped systems have ________ resonsnce peaks

Answer 33

flatter

Question 34

real exam question:
state the conditions for SHM (2m)

Answer 34

1m - The acceleration is proportional to the displacement

1m - the acceleration is in opposite direction to displacement

just remember a ∝ -x

Question 35

in the pndulmum practical:
how far do you displace the pendumum when performing the practical

Answer 35

1. less then 10 degrees (small angle)

Question 36

in the pndulmum practical:
how can you ensure you meause time peried accuretly(3)?

Answer 36

• measure 10T and then divide by 10 (reduce percentage uncertainty)
• use a fiducial marker (to reduce parallax error)
• meausre 3 x 10T (spot anomalies)

Question 37

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.

Answer 37

decreses, flatter, lost

decreses

Question 38

What is the phase diffrence between the veriation of displacment over time and the veriation of acceleration with time for a body

Answer 38

pie or 180degrees

e.g
max a is -max x
and
-max a is max x

think of a∝-x

Question 39

exam question:
state what is ment by simple harmonic motion (1mark)

Answer 39

• acceleration is preportinal to displacment
• acceleration is in the opposit direction to displacment

a∝-x

Question 40

velocity is ___ out of phase from x
acceleration is ____ out of pahse with x

Answer 40

90

180