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Archive for November, 2015

Today I thought I would share this classic Welsh song “Ti a dy ddoniau” (You and your skills), written by comedian and singer/songwriter/actor Ryan Davies. Ryan formed part of a comedy duo with fellow actor Ronnie Williams. They were popular on Welsh language TV in the 1970s, “Ryan a Ronnie” (Ryan and Ronnie) became so popular that it was transferred to an English language version. I remember watching both Welsh and English versions as a child.

Ryan (1937-1977) was born in Glanaman in Carmarthenshire (west Wales), and first performed professionally at the National Eisteddfod in 1966. “Ti a dy ddoniau” is my favourite Ryan Davies song, although it is possibly not his most famous. He is considered one of the giants of Welsh language TV entertainment, there is a bust of him in the foyer of the BBC studios in Llandaf (Cardiff) which I have seen many times on my visits there to do astronomy interviews.

Ryan Davies (1937-1977) was a Welsh actor, singer and comedian.  He was born in Glanaman in west Wales. He is best known for his TV comedy series "Ryan a Ronnie" (Ryan and Ronnie). He was also an accomplished singer and songwriter.

Ryan Davies (1937-1977) was a Welsh actor, singer, songwriter and comedian. He was born in Glanaman in west Wales. He is best known for his TV comedy series “Ryan a Ronnie” (Ryan and Ronnie). He was also an accomplished singer and songwriter. This is the cover of one of his CDs.

“Ti a dy ddoniau” is clearly written by a man who is very bitter. Lied to, made a fool of and hurt, the man is lashing back. Ryan himself married his childhood sweetheart and they remained married throughout his life; so I can only assume that he did not write these wonderful lyrics from personal experience. 

Here are the lyrics of “Ti a dy ddoniau”.

O ble gest ti’r ddawn o dorri calonne?
O ble gest ti’r ddawn o ddweud y celwyddau?
Ac o ble gest ti’r wên a’r ddau lygad bach tyner?
Ac o ble gest ti’r tinc yn dy lais?

Os mai hyn oedd dy fwriad, i’m gwneud i yn ffŵl,
Wel do, mi lwyddaist, mi lwyddaist yn llawn.
Ond yr hyn rwyf am wybod yn awr,
Dwed i mi, o dwed i mi,
Ble gest ti’r ddawn?

Rwy’n cofio fel ddoe ti yn dweud, “Cara fi nawr”
A minnau yn ateb fel hyn, “Caraf di nawr”.
Ond mae ddoe wedi mynd a daeth heddiw yn greulon,
Ac o ble, ac o ble, ble rwyt ti?

Os mai hyn oedd dy fwriad, i’m gwneud i yn ffŵl,
Wel do, mi lwyddaist, mi lwyddaist yn llawn.
Ond yr hyn rwyf am wybod yn awr,
Dwed i mi, o dwed i mi,
Ble gest ti’r ddawn?

Here is my attempt at a translation. As usual, I have gone for a literal translation, with no attempt to retain any rhythm or rhyme.

From where did you get the skill to break hearts?
From where did you get the skill to tell your lies?
And from where did you get that smile and those two sweet tender eyes?
And from where did you get the lilt in your voice?

If this was your intention, to make me a fool,
Well yes, you succeeded, you succeeded completely.
But what I want to know now,
Tell me, oh tell me,
From where did you get the skill?

I remember like yesterday your saying “Love me now”
And my answering like this, “I will love you now”.
But yesterday has gone and today has come cruelly,
Oh from where, oh from where did you get the skill?

If this was your intention, to make me a fool,
Well yes, you succeeded, you succeeded completely.
But what I want to know now,
Tell me, oh tell me,
From where did you get the skill?

I could not find a video on YouTube of Ryan performing this song, although there are versions sung by other artists. So, I have created this video, which is the definitive version; Ryan singing it with his longtime comedy and entertainment partner Ronnie. Enjoy!

Which is your favourite Ryan Davies song?

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Testing Einstein?

A very clear and timely explanation of one test of Einstein’s general theory of relativity – the search for gravitational waves. Cardiff University has a very active research group in this area.

johngribbinscience

There has recently been a flurry of media stories about experiments searching for gravitational radiation, usually with headlines about “testing Einstein’s theory”.  In fact, these experiments are testing our ability to measure gravitational radiation, because there is already compelling proof that this prediction of the general theory of relativity (which is itself exactly 100 years old as I write) is correct.  This extract from my book Einstein’s Masterwork (http://www.iconbooks.com/blog/title/einsteins-masterwork/) should make everything clear.  But the experiments are still hugely important.  If we can detect gravitational radiation directly, we will have a new way to study things like black holes, supernovas — and binary pulsars.

Massive objects, such as the Earth or a star, drag spacetime around with them as they rotate.  If they move back and forth, they can also generate waves in the fabric of spacetime, known as gravitational waves, or gravitational radiation, like the ripples you can make…

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Following on from my derivation of the moment of inertia of a disk, in this blog I will derive the moment of inertia of an annulus. By an annulus, I mean a disk which has the inner part missing, as shown below.



An annulus is a disk of small thickness t with the inner part missing. The annulus goes from some inner radius r_{1} to an outer radius r.

An annulus is a disk of small thickness t with the inner part missing. The annulus goes from some inner radius r_{1} to an outer radius r.



To derive its moment of inertia, we return to our definition of the moment of inertia, which for a volume element dV is given by


dI = r_{\perp}^{2} dm


where dm is the mass of the volume element dV. We are going to initially consider the moment of inertia about the z-axis, and so for this annulus it will be


I_{zz} = \int _{r_{1}} ^{r} r_{\perp}^{2} dm


where r_{1} and r are the inner radius and outer radius of the annulus respectively. As with the disk, the mass dm of the volume element dV is related to its volume and density via


dm = \rho dV


(assuming that the annulus has a uniform density). The volume element dV can be found as before by considering a ring at a radius of r which a width dr and a thickness t. The volume of this will be


dV = (2 \pi r dr) t


and so we can write the mass dm as


dm = (2 \pi \rho t)rdr


Thus we can write the moment of inertia I_{zz} as


I_{zz} = \int _{r_{1}} ^{r} r_{\perp}^{2} dm = 2 \pi \rho t \int _{r_{1}} ^{r} r_{\perp}^{3} dr


Integrating this between r_{1} and r we get


I_{zz} = 2 \pi \rho t [ \frac{ r^{4} - r_{1}^{4} }{4} ] = \frac{1}{2} \pi \rho t (r^4 - r_{1}^{4}) \text{ (Equ. 1)}


But, we can re-write (r^{4} - r_{1}^{4}) as (r^{2} + r_{1}^{2})(r^{2} - r_{1}^{2}) (remember x^{2} - y^{2} can be written as (x+y)(x-y)). So, wen can write Eq. (1) as


I_{zz} = \frac{1}{2} \pi \rho t (r^{2} + r_{1}^{2})(r^{2} - r_{1}^{2}) \text{ (Equ. 2)}


The total mass M_{a} of the annulus can be found by considering the total mass of a disk of radius r (which we will call M_{2}) and then subtracting the mass of the inner part, a disk of radius r_{1} (which we will call M_{1}). The mass of a disk is just its density multiplied by its area multiplied by its thickness.


M_{2} = \pi \rho t r^{2} \text{ and } M_{1} = \pi \rho t r_{1}^{2}


so the mass M_{a} of the annulus is


M_{a} = M_{2} - M_{1} = \pi \rho t r^{2}- \pi \rho t r_{1}^{2} = \pi \rho t (r^{2} - r_{1}^{2})


Substituting this expression for M_{a} into equation (2) above, we can write that the moment of inertia for an annulus, which goes from an inner radius of r_{1} to an outer radis of r, about the z-axis is


\boxed{ I_{zz} = \frac{1}{2} M_{a} (r^{2} + r_{1}^{2}) }

Comparison to the moment of inertia of a disk

As we saw in this blog, the moment of inertia of a disk is I_{zz} = \frac{1}{2} Mr^{2}. It may therefore seem, at first sight, that the moment of inertia of an annulus is more than that of a disk. This would be true if they have the same mass, but if they have the same thickness and density the mass of an annulus will be much less.

Let us compare the moment of inertia of a disk and an annulus for the 4 following cases.

    The same density and thickness, r_{1} = 0.5 r
    The same density and thickness, r_{1} = 0.9 r
    The same mass, r_{1} = 0.5 r
    The same mass, r_{1} = 0.9 r

The same density and thickness, r_{1}=0.5r

We are first going to compare the moment of inertia of a disk of mass M with that of an annulus which goes from half the radius of the disk to the radius of the disk (i.e. r_{1} \text{ the inner radius of the annulus, is } = 0.5 r.

For the disk, its mass will be


M = \rho t (\pi r^{2}) = \pi \rho t r^{2}


The mass of the annulus, M_{a}, will be this mass less the mass of the missing part M_{1}, so


M_{a} = M - M_{1} = M - \pi \rho t (r_{1})^{2} = \pi \rho t (r^{2} - (0.5r)^{2})=  \pi \rho t (1-0.25)r^{2}


M_{a} = \pi \rho t (0.75)r^{2} = 0.75 M


The moment of inertia of the disk will be


I_{d} = \frac{1}{2} M r^{2}
The moment of inertia of the annulus will be


I_{a} = \frac{1}{2} M_{a} (r^{2} + r_{1}^{2}) = \frac{1}{2} (0.75M)(r^{2} + (0.5r)^{2}) = \frac{1}{2} (0.75M)(1.25r^{2}) = \frac{1}{2} (0.9375) M r^{2}


So, for this case, I_{a} = 0.9375 I_{d}, i.e. slightly less than the disk.

The same density and thickness, r_{1}=0.9r

Let us now consider the second case, with an annulus of the same density and thickness as the disk, and its inner radius being 90% of the outer radius, r_{1} = 0.9r. Now, the mass of the missing part of the disk, M_{1} will be


M_{1} = \rho t (\pi r_{1}^{2}) = \rho t \pi (0.9r)^{2} = 0.81 \rho t \pi r^{2} = 0.81M


which means that the mass of the annulus, M_{a} is


M_{a} = M - M_{1} = M-0.81M=0.19M


The moment of inertia of the annulus will then be

I_{a} = \frac{1}{2}M_{a}(r^{2}+r_{1}^{2}) = \frac{1}{2}(0.19M)(r^{2}+(0.9r)^{2})=\frac{1}{2}(0.19M)((1.81)r^{2} = \frac{1}{2}(0.1539)Mr^{2}


and so in this case


I_{a} = 0.1539 I_{d}


which is much less than the moment of inertia of the disk.

The same mass, r_{1}=0.5r

In this third case, the mass of the annulus is the same as the mass of the disk, and its inner radius is 50% of the radius of the disk. This would, of course, require the annulus to either have a greater density than the disk, or to be thicker (or both). So, M_{a} = M. The moment of inertia of the annulus will be


I_{a} = \frac{1}{2} M(r^{2} + r_{1}^{2}) = \frac{1}{2} M(r^{2} + (0.5r)^{2}) = \frac{1}{2} M(r^{2} + 0.25r^{2}) = \frac{1}{2} M(1.25)r^{2}


I_{a}= 1.25 I_{d}

The same mass, r_{1}=0.9r

The last case we will consider is an annulus with its inner radius being 90% of the outer radius, but its mass the same. So, M_{a} = M. The moment of inertia of the annulus will be


I_{a} = \frac{1}{2} M(r^{2} + r_{1}^{2}) = \frac{1}{2} M(r^{2} + (0.9r)^{2}) = \frac{1}{2} M(r^{2} + 0.81r^{2}) = \frac{1}{2} M(1.81)r^{2}


I_{a}= 1.81 I_{d}

Summary

To summarise, we have

    The same density and thickness, r_{1} = 0.5 r, \; \; I_{a}=0.9375 I_{d}
    The same density and thickness, r_{1} = 0.9 r, \; \; I_{a}=0.1539 I_{d}
    The same mass, r_{1} = 0.5 r, \; \; I_{a}=1.25 I_{d}
    The same mass, r_{1} = 0.9 r, \; \; I_{a}=1.81 I_{d}


So, as these calculations show, if keeping the mass of a flywheel down is important, then a larger moment of inertia will be achieved by concentrating most of that mass in the outer parts of the flywheel, as this photograph below shows.



If keeping mass down is important, a flywheel's moment of inertia can be increased by concentrating most of the mass in its outer parts

If keeping mass down is important, a flywheel’s moment of inertia can be increased by concentrating most of the mass in its outer parts




In the next blogpost in this series I will calculate the moment of inertia of a solid sphere.

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At number 38 in Rolling Stone Magazine’s 100 greatest Beatles songs is “Blackbird”. Although credited to Lennon and McCartney, this 1968 song was not only composed solely by McCartney, but also he is the only one performing on the song. It appears on the Beatles’ White Album (officially known as “The Beatles”), an album I blogged about here as it is at number 10 in Rolling Stone’s list of the 500 greatest albums.

By the time the White Album was recorded during the summer of 1968, the rifts amongst the members of the Beatles were beginning to appear. Probably most (if not all) of the Lennon and McCartney songs on the album were composed separately, and often they would record their part of the song separately too, with the other members each adding their parts as overdubs. Hardly any of the songs were recorded with all four of them playing at the same time. Abbey Road studios effectively had Lennon, McCartney and Harrison each working in three separate studios.

“Blackbird” is a song about the struggle for civil rights in the United States. Unlike Lennon’s more direct “Revolution”, McCartney’s song is more oblique. In an interview in 2002 McCartney said

I remembered this whole idea of “you were only waiting for this moment to arise” was about, you know, the black people’s struggle in the southern states, and I was using the symbolism of a blackbird. It’s not really about a blackbird whose wings are broken, you know, it’s a bit more symbolic.




At number 38 in Rolling Stone Magazine's list of the 100 greatest Beatles songs is "Blackbird".

At number 38 in Rolling Stone Magazine’s list of the 100 greatest Beatles songs is “Blackbird”.



The melody of the song was inspired by Johann Sebastian Bach’s Bourrée in E minor, a lute piece which McCartney and Harrison used to attempt to play as teenagers to showcase their proficiency on the guitar. The melody of the song is beautiful, and it is my favourite McCartney song on the White Album.


Blackbird singing in the dead of night
Take these broken wings and learn to fly
All your life
You were only waiting for this moment to arise.

Blackbird singing in the dead of night
Take these sunken eyes and learn to see
All your life
You were only waiting for this moment to be free.

Blackbird fly Blackbird fly
Into the light of the dark black night.

Blackbird fly Blackbird fly
Into the light of the dark black night.

Blackbird singing in the dead of night
Take these broken wings and learn to fly
All your life
You were only waiting for this moment to arise
You were only waiting for this moment to arise
You were only waiting for this moment to arise.


Here is a video of this beautiful song. Enjoy!





Which is your favourite McCartney song on the White Album?

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A few years ago I blogged about a list in The Observer newspaper of the 10 best physicists. I felt it would be nice to write an up to date book about the greats in physics, and this list was as good as any. After enlisting the help of Brian Clegg, we set about writing a book with a chapter about each of the 10 physicists in The Observer’s list, along with a discussion in the last chapter as to whether we would choose the same 10. We agreed that nearly all physicists would include 4 names in their own list of the top 10 (buy the book to find out which 4!), but that the other 6 were much more subjective. Neither of us would have chosen the same 10 as are in this list.

"10 Physicists Who Transformed Our Understanding of the Universe" will be available in shops in early December

“10 Physicists Who Transformed Our Understanding of the Universe” will be available in shops in early December

As the back of the book says

Standing on the shoulders of giants…. 400 years of scientific breakthroughs, from Galileo to Feynman

Just to remind you, the list as presented in “The Observer” was

  1. Isaac Newton (1643-1727)
  2. Niels Bohr (1885-1962)
  3. Galileo Galilei (1564-1642)
  4. Albert Einstein (1879-1955)
  5. James Clerk Maxwell (1831-1879)
  6. Michael Faraday (1791-1867)
  7. Marie Curie (1867-1934)
  8. Richard Feynman (1918-1988)
  9. Ernest Rutherford (1871-1937)
  10. Paul Dirac (1902-1984)

We quickly realised that it would not be possible to write about e.g. Niels Bohr before writing about Ernest Rutherford, as Bohr’s work was based on the model of the atom which Rutherford introduced. The same is true of many others, including Isaac Newton, whose famous laws of motion were based on work that Galileo had done.

So, we re-ordered the list into chronological order, which gives us

  1. Galileo Galilei (1564-1642)
  2. Isaac Newton (1643-1727)
  3. Michael Faraday (1791-1867)
  4. James Clerk Maxwell (1831-1879)
  5. Marie Curie (1867-1934)
  6. Ernest Rutherford (1871-1937)
  7. Albert Einstein (1879-1955)
  8. Niels Bohr (1885-1962)
  9. Paul Dirac (1902-1984)
  10. Richard Feynman (1918-1988)
The back cover of the book

The back cover of the book

You can read more about the book by following this link, or you can pre-order your copy by following this link (this is the Amazon UK website, the book is also available in the US Amazon website by following this link)

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At number 22 in Rolling Stone Magazine’s list of the 100 greatest songwriters is Northern Irish singer/songwriter Van Morrison. Van Morrison is one of my favourite songwriters, he has written many memorable songs including “Bright Side of the Road”, “Brown Eyed Girl”, “Gloria”, “Moondance” and “Have I Told You Lately”.



At number 22 in Rolling Stone Magazine's list of the 100 greatest songwriters of all time is Van Morrison.

At number 22 in Rolling Stone Magazine’s list of the 100 greatest songwriters of all time is Van Morrison.



Morrison was born George Ivan Morrison in 1945 in Belfast, Northern Ireland. He first came to prominence as the lead singer of a Rhythm and Blues band Them, who formed in 1964. In 1965 Them had two hit singles in the DUK, “Baby, Please Don’t Go” (which got to number 10) was an old delta blues standard which had been popularised in the 1930s by Big Joe Williams. Them’s second hit single was “Here Comes the Night” (which got to number 2) and was written by American songwriter Bert Berns. “Gloria”, written by Morrison, was the B-side of “Baby, Please Don’t Go”, but has gone on to become a more famous song.

In the summer of 1966, towards the end of a tour of the United States, Them split up, and although they would later go on to reform, this was the end of Morrison’s involvement in the band. In 1967 he launched his solo career with the release of the single “Brown Eyed Girl”. This song appears on his first solo album, “Blowin’ Your Mind”, which was released by Bang Records without his knowledge after he had originally recorded eight songs which he thought would be released as four separate singles. Morrison then signed with Warner Brothers and in 1968 he released “Astral Weeks”. This is often considered his greatest album, and featured in my blog here about the 500 greatest albums of all time, as it is in that list at number 19.

With so many good songs to choose from, it has been difficult for me to choose just one, but I have decided on his first solo single, “Brown Eyed Girl”. It is beautiful example of Morrison’s wonderful lyrics and ability to write great music, and nicely displays his vocal talents as well.


Hey, where did we go
Days when the rains came ?
Down in the hollow
Playing a new game,
Laughing and a-running, hey, hey,
Skipping and a-jumping
In the misty morning fog with
Our, our hearts a-thumping
And you, my brown-eyed girl,
You, my brown-eyed girl.

Whatever happened
To Tuesday and so slow
Going down to the old mine with a
Transistor radio.
Standing in the sunlight laughing
Hide behind a rainbow’s wall,
Slipping and a-sliding
All along the waterfall
With you, my brown-eyed girl,
You, my brown-eyed girl.

Do you remember when we used to sing
Sha la la la la la la la la la la dee dah
Just like that
Sha la la la la la la la la la la dee dah
La dee dah.

So hard to find my way
Now that I’m all on my own.
I saw you just the other day,
My, how you have grown!
Cast my memory back there, Lord,
Sometime I’m overcome thinking about
Making love in the green grass
Behind the stadium
With you, my brown-eyed girl,
You, my brown-eyed girl.

Do you remember when we used to sing
Sha la la la la la la la la la la dee dah
Laying in the green grass
Sha la la la la la la la la la la dee dah
Dee dah dee dah dee dah dee dah dee dah dee
Sha la la la la la la la la la la la la
Dee dah la dee dah la dee dah la
D-d-d-d-d-d-d-d-d-d…



Here is a video of this wonderful song. Enjoy!





Which is your favourite Van Morrison song?

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In physics, the rotational equivalent of mass is something called the moment of inertia. The definition of the moment of inertia of a volume element dV which has a mass dm is given by


dI = r_{\perp}^{2} dm


where r_{\perp} is the perpendicular distance from the axis of rotation to the volume element. To find the total moment of inertia of an object, we need to sum the moment of inertia of all the volume elements in the object over all values of distance from the axis of rotation. Normally we consider the moment of inertia about the vertical (z-axis), and we tend to denote this by I_{zz}. We can write


I_{zz} = \int _{r_{1}} ^{r_{2}} r_{\perp}^{2} dm


The moment of inertia about the other two cardinal axes are denoted by I_{xx} and I_{yy}, but we can consider the moment of inertia about any convenient axis.

Derivation of the moment of inertia of a disk

In this blog, I will derive the moment of inertia of a disk. In upcoming blogs I will derive other moments of inertia, e.g. for an annulus, a solid sphere, a spherical shell and a hollow sphere with a very thin shell.

For our purposes, a disk is a solid circle with a small thickness t (t \ll r, small in comparison to the radius of the disk). If it has a thickness which is comparable to its radius, it becomes a cylinder, which we will discuss in a future blog. So, our disk looks something like this.



A disk of negligible thickness, with a radius of r.

A disk of small thickness t, with a radius of r



To calculate the moment of inertia of this disk about the z-axis, we sum the moment of inertia of a volume element dV from the centre (where r=0) to the outer radius r.


I_{zz} = \int_{r=0} ^{r=r} r_{\perp} ^{2} dm \text{ (Equ. 1)}


The mass element dm is related to the volume element dV via the equation
dm = \rho dV (where \rho is the density of the volume element). We will assume in this example that the density \rho(r) of the disk is uniform; but in principle if we know its dependence on r, \; \rho (r) = f(r), this would not be a problem.

The volume element dV can be calculated by considering a ring at a radius r with a width dr and a thickness t. The volume of this ring is just this rings circumference multiplied by its width multiplied by its thickness.


dV = (2 \pi r dr) t


so we can write


dm = \rho (2 \pi r dr) t


and hence we can write equation (1) as


I_{zz} = \int_{r=0} ^{r=r} r_{\perp} ^{2} \rho (2 \pi r dr) t = 2 \pi \rho t \int_{r=0} ^{r=r} r_{\perp} ^{3} dr


Integrating between a radius of r=0 and r, we get


I_{zz} = 2 \pi \rho t  [ \frac{ r^{4} }{ 4 } -0 ] = \frac{1}{2} \pi \rho t r^{4} \text{ (Equ. 2)}


If we now define the total mass of the disk as M, where


M = \rho V


and V is the total volume of the disk. The total volume of the disk is just its area multiplied by its thickness,


V = \pi r^{2} t


and so the total mass is


M = \rho \pi r^{2} t


Using this, we can re-write equation (2) as


\boxed{ I_{zz} = \frac{1}{2} \pi \rho t r^{4} = \frac{1}{2} Mr^{2} }

What are the moments of inertia about the x and y-axes?

To find the moment of inertia about the x or the y-axis we use the perpendicular axis theorem. This states that, for objects which lie within a plane, the moment of inertia about the axis parallel to this plane is given by


I_{zz} = I_{xx} + I_{yy}


where I_{xx} and I_{yy} are the two moments of inertia in the plane and perpendicular to each other.

We can see from the symmetry of the disk that the moment of inertia about the x and y-axes will be the same, so I_{zz} = 2I_{xx}. Therefore we can write



\boxed{ I_{xx} = I_{yy} = \frac{1}{2}I_{zz} = \frac{1}{4} Mr^{2} }

Flywheels

Flywheels are used to store rotational energy. This is useful when the source of energy is not continuous, as they can help provide a continuous source of energy. They are used in many types of motors including modern cars.

It is because of an disk’s moment of inertia that it can store rotational energy in this way. Just as with mass in the linear case, it requires a force to change the rotational speed (angular velocity) of an object. The larger the moment of inertia, the larger the force required to change its angular velocity. As we can see above from the equation for the moment of inertia of a disk, for two flywheels of the same mass a thinner larger one will store more energy than a thicker smaller one because its moment of inertia increases as the square of the radius of the disk.

Sometimes mass is a critical factor, and next time I will consider the case of an annulus, where the inner part of the disk is removed.

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