Physics

Velocity of COM

Unchanged, assuming no resultant external forces are acting on the system. Add equation.

Total momentum during a collision

Is conserved (unchanged) assuming no resultant external forces are acting on the system. Add equation.

Increase in mass towards centre of rotaion

I=mr²

r decreases, m increases, I decreases

OR

L=Iw

w increases, L is constant, I decreases

Ek (ROT) changes

• Equation

• Heavier COM causes I to decrease, hence w increases

• Ek (ROT) will decrease & Ek linear will increase

• Hence v increases so faster

L

Angular momentum is conserved no external resultant torques act.

Max speed in banked corners

• v=root(rgtan˚)

• If max speed is exceeded the Fc is too small to cause circular motion

• The object will move in a straight line at a tangent to the bend

SW - Strings

Created

Created by plucking, strumming, or rubbing a string.

SW - Strings

Length

Shorter strings have higher freq's due to a decreased wavelength. V=freq (increse) x wavelength (decrease)

SW - Strings

Tension

Tighter strings have higher freq due to increased speed. Wavelength and length are constant.

SW - Strings

Density

Lower density strings have higher freq's due to an increased speed.

SW - Strings

Temperature

Increase in temp causes strings to expand, reducing tension. Wavelength is constant (as ends of strings are fixed) so lower wave speed, thus lower freq of produced note.

SW - Strings

Pressing on strings

A node is formed, decreasing wavelength and increase freq. Length decreases. A different harmonic is created.

SW - Strings

For different notes/freq's to be played instruments must have either

- Strings of the same length, but different tensions and densities

or

- Strings of different lengths.

SW - Strings & Open Pipes

Equations

L=(#(WL)/2)

SW - All

Created

- Wave travels along & is reflected at the end

- Reflected wave interferes with og wave to produce a SW

- Wave must be at the fundamental frequency for pipe/string

- Waves meet in phase=constructive=antinode

- Waves meet out of phase=destructive=node (180˚ phase change)

SW - Open Pipes

Blowing in different spots

Wavelength changes depending on where you blow.

SW - Open & Closed Pipes

Longer pipe

Larger wavelength, freq decreases. Speed of sound is unchanged.

SW - Closed Pipes

Temp

Increase in temp causes speed of sound in air to increase. Wavelength is fixed (as length doesn't change), hence a higher freq note is produced.

SW - Closed Pipes

Different harmonics created

Blowing harder or opening or closing air holes along the pipe, creating an antinode, decreasing wavelength and increasing freq of produced note as waves travel less distance.

SW - Closed

Equations

L=(#(WL)/4)

More slits

• More slits create more wave sources that can interfere

• Sharper pattern

• Distance decreases

Brighter Pattern

- When light passes through slits, it’s diffracted and interference occurs

- More light can pass through with greater number of slits

- Constructive occurs (in phase waves)

- Path difference is a whole number of WL's

Dark regions

- Destructive occurs (out of phase waves)

- Path difference = (N-0.5)WL

Narrower Slits

Dark regions are wider

Slits are Closer Together

Fringes move further apart N(WL)=dsin˚,d decreases=sin˚ & ˚ increase=pattern covers more area. N(WL)/pathdifference & WL are unchanged. Less maxima, sharper & brighter pattern. More sources of interference.

Out of Phase Slits

Destructive interference occurs, so area with no light occurs

Brighter in the middle

Most constructive occurs as there is the most overlapping of waves

Red light

Longest wavelength, angle, path difference & greatest diffraction. Largest angle = forms maxima at largest angle, hence red light is formed on the outside of each spectrum.

Violet light

Smallest wavelength, angle, path difference & smallest diffraction. Smallest angle = forms maxima at smallest angle, hence violet light is formed on the inside of each spectrum.

Thickness of string

• Speed changes

• WL is unchanged

• F=(V/WL)= freq changed

Dopler - Source traveling betweeen two objects

• Towards and object: waves bunch up infront of sources, hence WL decrease (each wave is produced closer to the one before)

• Speed is constant.

• F=V/WL so freq increases.

• Visa versa for source traveling away from object.

• At object, they hear actual freq/constant freq as there is no dopler shift.

Beats

• Two waves w/ diff freqs interfere to become a new wave

• Beat freq is what is heard

• (f1-f2=beat freq)/Larger f minues smaller f.

• Loud spots occur when waves meet in phase and constructive interference occurs.

• Quiet spots occur when waves meet out of phase & destructive interference occurs 180˚ out of phase.

• Rise and fall in loudness is due to beats.

• Beats due to alternating constructive & destructive interference.

• Increasing one freq will decrease the beat freq.

SW- Closed

Uncovering a hole

• An antinode is created

• WL decreases as waves travel less distance

• V=(WL)f, v is unchanged, hence f increases

˚, d, x, s, WL

˚= angle from n=0 to n=1, etc

d= distance between slits

x= distance between n=0 and n=1, etc

s= number of slits per metre

WL= proportional to d

White light

It’s central as it’s formed from light passing straight through the slits and it’s made up of all the WL’s

There is no pathdifference to the central maxima as all colours are in phase so they constructivly interfere and combone to produce white light.

Dopler effected

• The closer the speed of the source is to the speed of the wave the greater the freq change (dopler shift) will be.

• Sound waves travel faster in air than more dense areas (e.g water).

• Hence greater freq change/ dopler shift occurs in air.

You have less mass, but need same I

I={mr² so mass must be distributed closer to the edge of the object

SHM occurs when accelration of object is

• Proportional to displacenemt from its equilibrium positon

• Directed towards equilibrium potion

ymax

A

vmax

AW

amax

-AW²

In time/same freq

• Resonance occurs

• Engergy put in has same freq as natural freq

• Amplitude increases

Harmonics created

• Must have either nodes or aninodes at both ends for even harmonics to be created

• Closed have ¼ WL so they produce node at one end, antinode at the other

Larger S/A vs Smaller S/A

Large: large I, small w

Small: small I, large w

L is conserved

If asked to find number of something

n + n + 1

If don’t know the angle and don;t have stuff to find it

It’s 90˚

Graph up to down =

• Higher to lower freq/increasing to decreasing freq/increasing in velocity towards or away for both.

• Actual freq is where observer is.

• Say how graph shows this.

In COM x is

distance from the start one

Overtones

1st harmonic = ½ overtone

NEXT harmonic = 1st overtone

NEXT harmonic = 2nd overtone

etc

Fundamental Freq

f=(harmonic #)fo

e.g 3rd harmonic: f=3fo

Forces at top vs bottom (both)

• Fc is provided by Fnet

• Fg acts downwards and is constant

Forces at top vs bottom (top)

• Fc is directed downwards towards centre of circle

• Fr is directed upwards and must be smaller than Fg for Fg to provide Fc

• Fg is directed to centre of the circle Fc=Fg-Fr

Forces at top vs bottom (bottom)

• Fc is directed upwards towards centre of circle

• Fr is directed upwards and must be larger than Fg so Fr can provide Fc

• Fg is directed to away from centre of the circle Fc=Fr-Fg

Energy from top to bottom

Ep=Ek(ROT)+EK(LIN) - w=(v/r)²

𝒯

(Curl t is)

Tension

If not easily given ˚/radians do:

d=r˚

Resonance

• Occurs when object is shaken at the natural freq so oscillation builds up.

• Freq of (object making sound) matches natural freq of shaking object.

• So fewer engergy is loss.

• Max amplitude and rattle occurs.

Diffraction

Spreading out of waves as they go through a gap.

Tan =

Tan = ˚/L

y, v, a

In radians

Top eq’s: start at equilibrium

Bottom eq’s: start at end

Reference circles ˚

˚ closer to end where thing started.

Fnet

Drawn horizontal

˚=tan^-1 (?)

(Fc/Fg)

Fc=Fg

I units

Kgm²

emf

Terminal voltage when no current is flowing

Graph emf stuff

V=emf, gradient = r

Krif rule

• If your going the going the same way as current, resistors is neg.

• Going into pos=-ve