How can one distinguish an OCD thought from a gut feeling?

About twenty five years ago I was going through a very difficult time with my OCD. It felt as though the walls were closing in and I was trapped. It reached a point where I was reluctant to leave the house as the intrusive thoughts were so pervasive. At the same time I got in touch with a physician-therapist who specialized in Cognitive Behaviour Therapy. Turns out that he was a God send.

I asked him this exact question. He told me that deep down one knows that the OCD thought is stupid. It has a completely irrational feel to it which is why giving into these thoughts by acting out the compulsion is so hurtful. The challenge with OCD was not so much the thought, in and of itself, but the triggering of a fear cycle that drives the compulsive behaviour. Breaking the linkage was the key to healing oneself. This realization helped me.

Gut feelings on the other hand don’t feel stupid. They are legitimate thoughts that may or may not have utility. Sometimes they serve us well other times they let us down. However they are not shrouded in the pain of the irrational that allows one to better identify the OCD intrusions.

Physics Answers - Part 3

 Physics Questions from Quora that I answered.

Can we perfectly predict the position of a planet in the solar system using Newtonian mechanics only?

All measurements in science carry with them a degree of error. In addition every scientific model has built in it several assumptions that do well to approximate reality but aren’t reality in and of themselves.

If you assume the ideal yes one can obtain a very accurate determination for planetary position especially in a two body problem. Three body systems are far more complex.

The fly in the ointment here with this question is the word ‘perfectly’. Its etymology forces us to reduce all uncertainty to zero. This is impossible as even in such an ideal system (with no margin of error) we cannot ignore Quantum Mechanical concerns (small as they are) nor do we have the luxury of freezing time to peg the position as exactly X. The world is an inherent system of flux and change.

Do all planets revolve around the sun with the same speed?

No they don’t. The closer a planet is to the sun the greater the pull of gravity on that planet. To maintain an orbit the planet therefore is forced to move at a higher velocity with decreasing orbital radius. The higher velocity provides for a greater inertia in motion (or linear momentum) to resist the inward gravitational pull.

The equation v = (GM/r)^0.5 describes the relationship where G = Universal Gravitation Constant. M =mass of the sun (kg) and r is the radius of orbit. v = orbital speed (or velocity magnitude).

As r decreases v increases. Notice as well that the value of v is independent of the planet’s mass.

The above equation can be derived by equating Newton’s Law of Universal Gravitation with the expression for the Net Centripetal Force and is related to Kepler’s Third Law of Motion.

Is Quantum physics physicists a good field to enter nanotechnology from?

Nanotechnology is one of those multi-disciplinary areas that draws in people from a variety of educational and experiential backgrounds. This makes sense as it has applications in electronics, medicine, materials, fluid mechanics, the military and environmental sciences to name but a few offshoots. Many engineering schools now have a specific department geared solely to nanotechnology. Nanotechnology Engineering

It has been an emerging discipline for some time and will likely play an important role in both the pure and applied sciences for the remainder of the 21st century.

Physicists with a strong background in quantum mechanics will always enjoy an advantage in nanotechnology as many of the effects that make the technologies possible rely heavily on quantum considerations viz. tunneling, wave-particle duality and various interactions at the matter-energy interface.

However there appears to be a demand as well for those with strong skill sets elsewhere. A molecular biology background and proficiency in computer coding cannot hurt.

What is the most important element in all of physics?

Hydrogen. It is the most abundant element in the universe and is the starting point for virtually every fusion system. It is through fusion that almost all of the other elements have been produced.

Western History 158: What was Manifest Destiny?

Democrat James K. Polk (1845-1849) was the country’s  11^th President succeeding John Tyler to the White House. Polk had been a strong ally of Andrew Jackson and was a one-time Speaker of the House of Representatives. He was also a former Governor of Tennessee. Polk's presidential term was highlighted for the expansion of US territory and the ascendancy of the unwritten doctrine of Manifest Destiny (coined in 1845). Proponents of  Manifest Destiny believed that the US had a God given right to expand across North America and thus extend American social and economic values (most notably Free Enterprise) across a far broader domain.

                                                  James Polk  Source: www.history.com

It was this philosophy that would play an important role in Polk’s thinking. In 1846 a settlement was reached with Great Britain known as the Oregon Treaty. This treaty set the border between the US and British North America for territory west of the continental divide at the 49^th Parallel (with the exception of Vancouver Island which was retained by Great Britain) ending an ongoing dispute that had existed since 1818. The US formalized its acquisition of the area that would become the states of Washington and Oregon. The 49^th parallel would eventually become the border between the US and  the later nation of Canada.

In 1845 the Republic of Texas was finally annexed into the United States. It would become the Union’s 28^th state. Texas had earlier on rebelled against the centralist Mexican authority  in 1836 and after a brutal struggle that saw  heroics at the Battle of the Alamo and then a final victory at the San Jacinto had earned a de facto Independence from Mexico (outlined in the Treaty of Velasco).  Its First and Third President was Sam Houston..

An artist's impression of the spirit of Manifest Destiny    source: www.newsweek.com

Relations with Mexico however deteriorated resulting in the Mexican-American War (1846-1848).  US forces were victorious and with the signing of the Treaty of Guadalupe Hidalgo the US acquired vast amounts of territory north of the Rio Grande that would eventually become the states of California, New Mexico (roughly half of the modern day area), almost all of Arizona, Nevada, Utah and Colorado. This combined territory was collectively known as the Mexican Cession. Financial claims were settled and Mexico was forced to recognize US sovereignty over Texas. The War itself  saw the US invasion of Mexico and the capture of Mexico City by the forces of General Winfield Scott.

Territory of  Guadalupe Hidalgo source: https://www.ssc.wisc.edu/

However far from being a win for the United States the newly acquired territory would in the short term cause more domestic turmoil as it further highlighted the slavery debate by bringing to the fore the ever pressing issue of whether slavery should be extended into the newly acquired territory.

From a historical perspective Polk is seen as one of the most competent American Presidents. The territorial acquisitions did much to bolster this claim (that was given an added boost by the California Gold Rush) and he largely avoided the scandals that had dogged other Presidents. Polk adhered to his original pledge that he would only be a one-term President and  was succeeded by Zachary Taylor who was a military hero from the Mexican-American War but was not Polk’s choice for the White Office (he preferred Lewis Cass). Polk passed away soon after leaving office.

Western History 157: Who was Andrew Jackson and what were the key events of his Presidency?

Carolina native Andrew Jackson was the seventh President of the United States.  Coming from wilderness /frontier stock Jackson  served in the Revolutionary  War as a patriot courier at the age of 13. Orphaned a year later he took to studying law under the tutelage of his uncle becoming a prosecuting attorney at the age of 21. A successful law practice eventually allowed him to become a wealthy landowner.  In 1798 Jackson was elected to the House of Representatives as the first member from Tennessee. He would serve as judge until 1804 before distinguishing himself in the War of 1812 where he led American troops to an unlikely victory over the British at the Battle of New Orleans.

Always popular with his troops Jackson earned himself the nickname ‘Old Hickory’ as he was believed to be as tough as old hickory wood. Later on he would be involved in leading troops in the First Seminole War where he likely over stepped his orders by invading Spanish-controlled Florida. In Congress he was censured for his action but was ironically defended by John Quincy Adams, his future rival and the sixth President of the United States. 

When Florida reverted to American control in 1819 Jackson served in the capacity as its military governor for a short period in 1821. A year later he was elected to the US Senate and then in a bold move he stood for the Presidency in 1824. However in an election manipulated by supposed backroom dealings (known as the Corrupt Bargain) Jackson was denied the Presidency at the expense of John Quincy Adams.

Andrew Jackson - President (1828-1836) source: britannica.com

Jackson had a strong popular following  but  was derided by his opponents as a ‘jackass’-  a moniker that he accepted. This would later become the definitive symbol of the Democratic Party that he eventually founded.As President Jackson was known for his use of veto power to spearhead policy (as opposed to its traditional use as an instrument to resist unconstitutional change). He rallied against corruption and had a great deal of contempt for the Electoral College, but at the same time he tended to reward his followers through a system of spoils.

A cartoon mocking Andrew Jackson\s spoils system source: Library of Congress

Jackson’s earliest battle centered on the nature of the Second Bank of the United States. He saw it as a corrupt institution, controlled by elitist bankers, who manipulated the economy with paper currency. In the 1832 election he ran against Henry Clay who supported the renewal of the Bank’s charter. Jackson took the reverse position and carried the day. His stance here would lead eventually to the bank’s eventual demise in 1836.

However it was the nullification crisis that would in a sense define his Presidency. The passing of federal tariffs in 1828 and 1832 were opposed by politicians in South Carolina particularly who saw this as a move favoring Northern manufacturers at the expense of their state. Sentiments reached a fever pitch with the state passing a resolution to declare such tariffs as null and void. There were calls for secession with Jackson’s Vice President Calhoun  breaking with the President over this controversial issue.

Jackson himself was not a fan of the tariffs (he believed they were too high) but did not wish to see Federal Law undermined. Calhoun for his part would resign  and stand against Jackson for the presidency. He  was replaced by Martin Van Buren who would eventually become  the country’s Eight President. Fortunately a compromise was passed. The tariffs would be lowered but Jackson  earned future Presidents the right (via a provision) to enforce federal law. This would have significance in the lead-up to the American Civil War.

A very dark time in Jackson’s Presidency centered on his use of the Indian Removal Act of 1830 that forced  the mass displacement of various  Native Americans tribes from their ancestral lands to territory west of the Mississippi River. The Cherokee tribe for one suffered greatly here as they driven under gun point to relocate to Arkansas. The horrendous event has been immortalized as the Trail of Tears. It impacted 15,000 Cherokee causing about 4,000 deaths.

When Jackson left office in 1836 the economy was struggling. The inability of the banks to meet the gold and silver demands for the payment of public land (a result of Jackson’s opposition to paper money) led to financial shortages that would culminate in the Panic of 1837.

Overall Jackson had a mixed record as president although he is generally considered to have had a significant impact on American history for the reasons described above. The populist appeal of his Jacksonian Democracy would resonate nationally as it directly challenged the traditional power hierarchy that had dominated the country's politics since the War of Independence.

How is it possible that Floyd Patterson managed to go 12 rounds with Muhammad Ali while Sonny Liston knocked Floyd Patterson out in the first rounds?

 Asked on Quora. My Answer.

You see such a phenomenon in all sports not just boxing. Certain figures match up better against one another. Even on a team level squads don’t really follow a linear pattern when facing each other on a one-to-one basis. Take soccer - Brazil in the 90s struggled against minnows Norway but had no problem dealing with powerhouses such as England, Italy and the Netherlands.

In tennis South African Wayne Ferreira had a great record against Pete Sampras but was never good enough himself to win a Grand Slam. Sampras won 14 big ones. Henri Leconte, the Fereirra of the 80s, was also capable of getting under the skin of eight time Grand slam winner Ivan Lendl. There are numerous other examples.

As another answer mentioned style is key. In boxing though you also have the added variable of the so-called ‘lucky’ punch that can turn a result on its head and give the bookies somewhat of a headache.

However with respect to the Liston v Patterson match-up the former’s sheer power and extensive reach meant that Patterson couldn’t move in close enough to hurt his opponent. Liston had him where he wanted and this dictated the final outcome for both fights. The two Foreman-Frazier fights followed a similar pattern in favour of Big George.

When Patterson fought Ali (then Cassius Clay) in 1965 the Lip gave his opponent far more latitude than Liston did. Patterson could therefore exercise his skill set more effectively despite the fact that he is believed to have had a back injury at the time of the fight.

Unlike Liston, Ali’s style was not based on the dominance of power hitting. He favoured a purer form of pugilistic finesse that involved the triple arsenal of bob, weave and punch. Ali still dictated conditions but these conditions were more favourable to Patterson.

Some have suggested that Ali was toying with his opponent for entertainment and could have ended the fight much earlier. Patterson, some would say, was a sucker for punishment and Ali took advantage of this. I think that is a bit harsh toward both Patterson and Ali. No fighter seeks to go 12 rounds with an opponent if they have the opportunity to end a fight earlier. The final outcome was likely never in doubt but Patterson had enough boxing smarts to force himself onto the inside of Ali and prolong the eventual.

What were the greatest Boer victories?

 I was hoping to answer a question on Quora regarding the Anglo-Boer War. This one worked out well.

As someone who was born in South Africa I always welcome questions on my country of birth. I assume by Boer War that you mean the Second Anglo-Boer War. The First Boer War was fought between 1880–1881 and was crowned by the Boer victory at the Battle of Majuba.

The Second-Anglo-Boer (1899–1902) was somewhat of a critical moment in both the history of South Africa as well as that of the British Empire.

From a South African perspective the war impacted the power balance that would define the country for the next century (English v Afrikaans). With respect to the Empire it brought to an end the Era of Splendid Isolation. Soon afterwards London would sign treaties with Japan (1902), France (1904) and Russia (1907). The War showed how stretched British resources could become in the face of a credible regional threat.

The Boers , who were known for their ace markmanship, quality of troops and organizational skills had several victories against the British. The earliest of these occurred at the battles of Kraaipans and Ladymith (the battle not the siege). However the most impressive of all Boer victories were the three triumphs of the so-called Black Week (10th-17th December 1899).

These were the battles of Stormberg, Magersfontein and Colenso. While less than three thousand troops died in all three clashes (for both sides) the events of this hell week forced a rethink in Imperial policy. Another Boer victory would follow a month later at the Battle of Spion Kop.

British Troops fighting during Black week source: historywm.com

However the Battles of Black week were important, For one it expedited the removal of Sir Redvers Buller who was already blamed for the debacle at Ladysmith and his replacement by Lord Roberts who in turn made Herbert Kitchener (of WWI fame) his chief of staff. The British would increase their troops mobilization drive extending their efforts throughout the Empire drawing recruits from Australia, New Zealand and Canada. They would now win with numbers.

Boer soldiers source:”Guardian

Eventually the enhanced mobilization would bear fruit. The Boers soon realized that they could no longer defeat the numerically superior British forces in open combat so they transitioned toward a guerrilla war that in itself was rather effective in the short run. Stunned once again the British then responded with a scorched Earth policy that brought about the surrender of the Boers in 1902. The signing of the Treaty of Vereeniging finally ended the war.

However in retrospect the Boers gave the British a bloody nose and rubbed their face in it on several occasions. Yes the British would ultimately persevere but at a cost of men, material and morality. The burning of Boer farms and the forced relocation of Afrikaner women and children into the original concentration camps was both tragic as it was ethically regressive.

Military lessons learnt would pay dividends during World War One but the price that the Empire paid was not cheap. The British Empire had their prototype Vietnam..

Sources:

1. Gooch, John (23 October 2013). The Boer War: Direction, Experience and Image. Taylor & Francis. ISBN 978-1-135-27181-7.

2. Scholtz, Leopold (2005). Why the Boers Lost the War. Basingstoke: Palgrave-Macmillan.. ISBN 978-1-4039-4880-9

Western History 156: How did the Presidents James Madison and James Monroe impact the United States during their terms in office?

James Madison (1809-1817), another Virginian followed Thomas Jefferson as President of the United States. Madison had enjoyed a strong friendship with Thomas Jefferson and was in 1780 the youngest delegate to the Continental Congress. A strong analytical thinker Madison was one of the three Authors of the vert well respected Federalist papers. The other two were Alexander Hamilton and John Jay.

Worth noting is that Madison was initially not supportive of the Bill of Rights as he believed there were enough constitutional guarantees to render them moot. However he changed his mind as he felt it was a necessary compromise to ensure ratification of the Constitution. His role in the drafting of the US constitution was pivotal. Between 1801-1809 Madison served as Thomas Jefferson’s Secretary of State. Like Jefferson he was a member of the Democratic-Republican Party.

Madison’s term in office was overshadowed by the War of 1812 that we have discussed earlier. He spearheaded the US through this difficult time and was aided considerably by his wife Dolly, a strong and warm first lady who is widely accredited with defining the role.

During his term in office the Second Bank of the United States was created (1816) and the country issued strong protective tariffs. Like all antebellum US Presidents he struggled with the issue of  slavery. Madison believed that the impact of slavery would become less significant over time as the country spread westward. 

He was however one of the founders of the American Colonization Society that established the state of Liberia for freed slaves. Madison himself was not an intellectual supporter of slavery and believed that the institution had imposed an unnecessary class structure on the south. However he also saw no optimal pathway that would facilitate its removal in the contemporary. In terms of the slavery debate at the time he is seen as somewhat of an intermediate between opposing view points.

James Madison source: britannica.com

James Monroe (1817-1825) succeeded Madison as President bringing to four the number of Presidents from the State of Virginia. Like Madison Monroe was a Democratic-Republican who had blazed a trail to the White House as Secretary of State. His period in office is known as the Era of Good Feeling. Monroe signed the Missouri Compromise (1820) that brought Missouri into the Union as a slave state while prohibiting all slavery north of the 36°30′ parallel.  

In 1819 the Monroe signed the Adam-Otis agreement with Spain that secured Florida for the United States. Like Madison he advanced the Liberia settlement initiative.  Monroe’s term in office was not without problems. The US suffered through an economic crisis known as the Panic of 1819 that was made worse by a great deal of economic speculation.

James Monroe source: biography.com

However it was the collective policy of what would become the Monroe Doctrine that seems to be the greatest legacy of Monroe’s Presidency. Oddly enough the term ‘Monroe Doctrine’ was only used for the first time in 1850. 

The doctrine enforced the notion of a robust American foreign policy. European countries were warned that any intervention in the politics of the Americas (both North and South) would be seen as an affront to the United States. In doing so Monroe effectively guaranteed the independence of the recently independent Latin America countries from their colonial mother countries and established much of the Western Hemisphere as a definitive American sphere of influence. The Doctrine has influenced American foreign policy ever since.

 

Did Europe act irresponsibly during the Cold War with respect to their defensive needs?

 (Asked on Quora). My answer.

Yes and No. People have to remember that the double hit of World War One and World War Two has thrown Europe off their much vaunted podium as the vanguard of Western Civilization. The continent has been in relative decline for close to a century now and this aspect of a weakening was reflected and amplified by the Cold War.

It was to be expected. The losses in both wars were immense and the various ruling elites on the continent were found wanting. After 1945 Western Europe in particular was exhausted. Former powerhouses, the UK, France and Germany (now divided) were a shell of what they once were with the locus of global power in the West shifting across the Atlantic to the United States.

The national economies of many Western European countries were wrecked and although they were in several cases resuscitated (West Germany especially) as a function of such American initiatives as the Marshall Plan a great deal of the robustness of these societies had been lost.

The appetite for war, let alone the will to extend one’s influence globally (a feature of Europe’s glory in the 19th century), had been emptied and in the face of growing Soviet aggression Western Europe offered scant resistance to Moscow. Most of Eastern Europe had already succumbed to the onslaught of the Red Army with the communist threat in Greece and Turkey only barely curtailed (Three cheers for the Truman Doctrine).

If the United States did not act as the chief stop gap to further expansion it is conceivable that the Soviet Juggernaut could have spread Westwards gobbling up Austria and much of the remainder of Germany in its wake. Who knows what may have followed in the absence of an American deterrence? France was in no position to resist the Soviets. Neither were the Low countries nor Italy for that matter. The British population had no stomach for a war on the continent and who can blame them? The largely land based war that defined WWI was the beginning of the end of Britain as a global power and its repercussions were all too clear.

It was only the US that could guarantee European security. However Washington was not prepared to do so alone which is why NATO was formed in 1949. Included in the anti-Soviet alliance were most of the Western European countries plus Canada but it was clear from the get go that the US would do the heavy lifting. No other country had the military capacity to do so. It was as simple as that.

So did Europe act irresponsibly? I don’t believe they did. At least so initially. When pushed they didn’t have much to offer post WWII. The wars of the 20th century had gutted the major Western European powers. However we have moved on from those dark days in the late 40s, 50s and 60s. While Europe is no the longer the epicenter of global economics many Western European countries have benefited immensely by having the US taxpayer essentially fund their security. They are also wealthier than they were in 1945.

With few exceptions these countries have become over-reliant on Uncle Sam, with their own defense budgets falling way short of where they ought to have been in the face of an external threat. In this respect they have acted irresponsibly and until recently most American Presidents have not pushed the issue. Hopefully Biden will continue where Trump left off. There is nothing good about being a Free loader. Strong relationships are built on mutual contributions that are not one-sided. Western Europe needs to own more of its security by taking national responsibility.

Is Biden strong enough to run a divided country?

 (My answer on Quora).

Joe Biden by himself is likely not strong enough. He enters as a tainted candidate with personal and political challenges looking more like accidental presidential advisor Chauncey Gardiner than any other POTUS before him. He is that weak and obviously flawed.

Chauncey Gardiner - A Character from the movie Being There starring Peter Sellers source: The Published Reporter.

However this could be immaterial. Biden will likely be no more than a figurehead in the Administration that carries his name anyway. His function was to serve as a placeholder alternative for an election that was a referendum on Trump’s personality and it seems to have worked. Job done….for now.

The bigger question then is will the cabal of powers behind Biden be up to the task? Can they serve to make the former Vice President seen more than just a talking head? C’mon man it won’t be easy.

For starters as the question implied the nation is extremely divided. Donald Trump lost narrowly in four swing states despite winning over 74 million votes. To many of his supporters the election was stolen. Biden is more of an asterisk President than anything else.

The GOP has narrowed the differential in the House and could very well secure the Senate (we will see in January). In addition SCOTUS now has a conservative/originalist majority with three Trump appointees on the bench. The Appeals and District courts have also been strengthened to make it more difficult for the Progressive agenda to see the light of day. State legislatures lean heavily towards the GOP who also control 26 of the 50 governorships.

There is in place the foundation for a solid resistance against any radical overhaul and Biden’s handlers know this. If they run too far to the left then the Donks will likely be crucified in 2022. However on the other hand they owe the radical element of their party a great deal. Without the buy in from the Party’s left wing and the endorsement of the Sanders’ camp, Biden would likely be this era’s version of Robert Dole. They will expect payback and rightfully so.

Source: The Colombus Dispatch

So far the cabinet appointees have not been kind to the Bros but this will have to change. There is a clear fault line here within the Democratic Party and it will not retreat mildly into the sun. When you build a coalition on Inter-sectional politics you will eventually have to pay the piper and it won’t come cheaply.

After the honeymoon period ends (and it won’t last long) the road could be primed for a rocky divorce. The Establishment backers know this and they will answer it with the necessary Danegeld. However it may get messy especially if the radicals feel scorned and the sin offerings are not adequate.

Biden has some likable qualities that may help him but he inherits a country where calls for unity ring hollow. The anger around the lockdowns haven’t helped and if the middle class feel as though they have been set adrift in favour of Biden’s multi-national corporate cronies it will not bode well for his administration. The United States stands at a cross-roads with a media that has lost the trust of the populace.

Biden Inc. could be facing strong opposition on two fronts from both the left and the right as the center shrinks. Globalism is looking a bit war weary and its brand utility may be on the wane. A worsening economy could bring matters to a head which may force the brain trust that runs will run his administration to cut their losses when they can. He could be their first victim. We will wait and see.

In any case where does this leave the nation in the mean time? Well we can’t say for sure. Biden could do much by taking a strong stand against China and by extension the CCP on both trade and national security issues. Beijing’s behaviour during the Covid-19 pandemic has been problematic and disingenuous however I am not convinced that he will.

The Democrats have had Russia in their cross-hairs for awhile and they may use the excuse of the Solar Wind hack to up the ante against Moscow. This could backfire. A conflict here would suit Beijing to a tea and may not necessarily benefit the United States as some seem to think. Putin is a menace and should be taken to task but the US needs to exercise full diligence before acting rashly.

All in all his backers will have to proceed with caution. The margin of error is slim and people’s patience has worn thin. The Democrats weaponized every avenue of power in sight to take down Trump however the unintended (or intended) consequences may be more than they bargained for. The greatest tragedy would see the United States take a giant step on the road to decline while the Biden backers fiddle behind the scene.

Source: Daily Herald

G-d bless America.

Physics Answers - Part 2

Two objects have the same kinetic energy. Which one has the bigger magnitude of momentum?

The more massive object will have a greater linear momentum.

Lets look at an example here: Take two objects. One of mass 3 kg and the other of mass 1 kg. Assume they have the same Ek = 9 J.

Since Ek = 1/2m(v^2) we can rearrange and solve for v therefore v = (2*Ek/m)^0.5.

For the more massive object v = 2.45 m/s

For the less massive object v = 4.24 m/s.

Now lets go to linear momentum

p for more massive object = mv = (3)(2.45) = 7.35 kgm/s

p for the less massive object = mv = (1) (4.25) = 4.25 kgm/s.

So why is it the case? The reason is that in order for Ek to be equal a high mass must be offset with a lower v squared. Sounds good. However linear momentum is the product of mass and velocity. Velocity on its own cannot offset mass to the extent that velocity squared can in the Ek equation therefore the linear momentum of the larger object dominates. Think of this as the power of squares.

Does direction matter in momentum?

Very much so. Linear momentum is a vector quantity and therefore has a directional aspect to it. Here is an example to think about. Two carts with the same mass moving toward each other with the same speed have equal magnitudes of linear momentum. However their velocity vectors are 180 degrees reversed which implies that the linear momentum of each have opposite directions.

Remember that the linear momentum of an object is the product of its mass and its velocity. This means that the total momentum for the system - where the system is defined as both cars only - is equal to 0 kgm/s. Momentum vectors cancel each other out for the system as a whole. Not so for each cart specifically.

Could the universe exist without gravity? If so how would it look?

Yes you could have such a universe hypothetically however it will look extremely different to anything we could conceive of. You will for one have no large clumping of matter. So don’t expect to find any planets, stars, stellar clusters, galaxies, galactic clusters etc.

You would still likely have atoms as the nuclei of these are hold together by the nuclear forces (strong and weak) with the electromagnetic force ensuring that the electrons are attracted to the nuclei. Other than that…Who knows? A giant particle soup makes sense. Also without gravity one could expect this universe to have no resistance to expansion so that it will likely proceed to an eventual big rip at a faster rate.

What is the difference between momentum and Inertia?

Inertia is the property of matter that resists a change in motion or acceleration. It is directly related to the mass (sometimes called Inertial Mass) of the object and is measured in kilograms. Mass of course, in the classical world, refers to the amount of matter an object contains and is a scalar quantity.

Linear Momentum is a vector quantity and can be viewed as essentially ‘intertia-in-motion’. It is the product of the object’s mass and its velocity. It has units of kg.m/s or N.s.

In the world of modern physics - the linear momentum of a massless particle (eg. a photon) can be determined by dividing Planck’s constant (h) with the wavelength of the photon. This expression comes from a rework of the linear momentum equation based using the notion of mass-energy equivalency.