The Two Scalars — phryzby

solved Vectors

Q. Which two of these are scalars?

How it's solved

Solved with Vectors

Working

force: a vector, it has a direction
angular momentum: a vector, it has a direction
work: a scalar, a size alone
current: a scalar, a size alone
linear momentum: a vector, it has a direction
electric field: a vector, it has a direction
average velocity: a vector, it has a direction
magnetic moment: a vector, it has a direction
relative velocity: a vector, it has a direction

Conclusion

Work is an amount of energy handed over, with no direction of its own. Current flows along a wire, but it adds like a number, not like arrows, so it is a scalar too.

The web of concepts

given read from the words equation asked

The Ruby that solves it

The question and its solution are small Ruby files. The engine runs them.

question.rb

1require_relative "../physics"23question :the_two_scalars do4  kind :mcq5  describes "Which two of these are scalars?"67  option "force"8  option "angular momentum"9  option "work"10  option "current"11  option "linear momentum"12  option "electric field"13  option "average velocity"14  option "magnetic moment"15  option "relative velocity"16end

solution.rb

1require_relative "../questions/the_two_scalars"2require_relative "../science/motion_in_a_plane/vectors"34solve :the_two_scalars, using: Vectors do5  answer options.select { |o| o.content.to_quantity.scalar? }67  conclusion "Work is an amount of energy handed over, with no direction of its own. Current " \8             "flows along a wire, but it adds like a number, not like arrows, so it is a scalar " \9             "too."10end

playground.rb

1require_relative "../solutions/the_two_scalars"23play_with :the_two_scalars do4  title "The Two Scalars"5end

The laws it drew on

quantity	written	units	within	from
volume	$volume$	—	—	Vectors
mass	$mass$	—	—	Vectors
speed	$speed$	—	—	Vectors
density	$density$	—	—	Vectors
number of moles	$n$	—	—	Vectors
angular frequency	${angular}_{frequency}$	—	—	Vectors
work	$work$	—	—	Vectors
current	$current$	—	—	Vectors
temperature	$temperature$	—	—	Vectors
pressure	$pressure$	—	—	Vectors
time	$time$	—	—	Vectors
power	$power$	—	—	Vectors
total path length	$s$	—	—	Vectors
energy	$energy$	—	—	Vectors
gravitational potential	${gravitational}_{potential}$	—	—	Vectors
coefficient of friction	$μ$	—	—	Vectors
charge	$charge$	—	—	Vectors
acceleration	$acceleration$	—	—	Vectors
velocity	$velocity$	—	—	Vectors
displacement	$displacement$	—	—	Vectors
angular velocity	${angular}_{velocity}$	—	—	Vectors
force	$force$	—	—	Vectors
angular momentum	${angular}_{momentum}$	—	—	Vectors
linear momentum	$p_{lin}$	—	—	Vectors
electric field	${electric}_{field}$	—	—	Vectors
average velocity	${average}_{velocity}$	—	—	Vectors
magnetic moment	${magnetic}_{moment}$	—	—	Vectors
relative velocity	$v_{AB}$	—	—	Vectors
impulse	$impulse$	—	—	Vectors
first vector	$A$	—	0 … ∞	Vectors
second vector	$B$	—	0 … ∞	Vectors
angle between	$φ$	—	0 … 3.142	Vectors
resultant	$R$	—	0 … ∞	Vectors
resultant direction	$β$	—	0 … 3.142	Vectors
direction	$α$	—	-3.142 … 3.142	Vectors
x component	$A_{x}$	—	—	Vectors
y component	$A_{y}$	—	—	Vectors

A = \sqrt{{A_{x}}^{2} + {A_{y}}^{2}}

magnitude from components

R^{2} = A^{2} + B^{2} + 2 \cdot A \cdot B \cdot \cos φ

law of cosines

R \cdot \sin β = B \cdot \sin φ

law of sines

R \cdot \cos β = A + B \cdot \cos φ

along the first

A_{x} = A \cdot \cos α

resolved along x

A_{y} = A \cdot \sin α

resolved along y