Which Are Vectors

play phryzby with physics

Q. Which of these are vectors? expects D, G, I, J

What the draft establishes

Fills in once a draft is checked.

The web of concepts

given read from the words equation asked

The equations it used

None yet.

The playground

The solution

Solved with Vectors

Working

volume: a scalar, a size alone
mass: a scalar, a size alone
speed: a scalar, a size alone
acceleration: a vector, it has a direction
density: a scalar, a size alone
number of moles: a scalar, a size alone
velocity: a vector, it has a direction
angular frequency: a scalar, a size alone
displacement: a vector, it has a direction
angular velocity: a vector, it has a direction

Conclusion

A vector needs a direction as well as a size. Speed is how fast; velocity is how fast and which way. Angular frequency counts turns in a time, while angular velocity points along the axis of the turning.

The Ruby

1require_relative "../physics"23question :which_are_vectors do4  kind :mcq5  describes "Which of these are vectors?"67  option "volume"8  option "mass"9  option "speed"10  option "acceleration"11  option "density"12  option "number of moles"13  option "velocity"14  option "angular frequency"15  option "displacement"16  option "angular velocity"17end

1require_relative "../questions/which_are_vectors"2require_relative "../science/motion_in_a_plane/vectors"34solve :which_are_vectors, using: Vectors do5  answer options.select { |o| o.content.to_quantity.vector? }67  conclusion "A vector needs a direction as well as a size. Speed is how fast; velocity is how " \8             "fast and which way. Angular frequency counts turns in a time, while angular " \9             "velocity points along the axis of the turning."10end

1require_relative "../solutions/which_are_vectors"23play_with :which_are_vectors do4  title "Which Are Vectors"5end

The laws

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