play phryzby with physics

Which Are Vectors

solved Vectors

Q. Which of these are vectors?

Select all that apply.

How it's solved

Solved with Vectors

Working
  1. volume: a scalar, a size alone
  2. mass: a scalar, a size alone
  3. speed: a scalar, a size alone
  4. acceleration: a vector, it has a direction
  5. density: a scalar, a size alone
  6. number of moles: a scalar, a size alone
  7. velocity: a vector, it has a direction
  8. angular frequency: a scalar, a size alone
  9. displacement: a vector, it has a direction
  10. 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 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 :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
solution.rb
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
playground.rb
1require_relative "../solutions/which_are_vectors"23play_with :which_are_vectors do4  title "Which Are Vectors"5end
The laws it drew on
quantitywrittenunitswithinfrom
volumevolume——Vectors
massmass——Vectors
speedspeed——Vectors
densitydensity——Vectors
number of molesn——Vectors
angular frequencyangularfrequency——Vectors
workwork——Vectors
currentcurrent——Vectors
temperaturetemperature——Vectors
pressurepressure——Vectors
timetime——Vectors
powerpower——Vectors
total path lengths——Vectors
energyenergy——Vectors
gravitational potentialgravitationalpotential——Vectors
coefficient of frictionμ——Vectors
chargecharge——Vectors
accelerationacceleration——Vectors
velocityvelocity——Vectors
displacementdisplacement——Vectors
angular velocityangularvelocity——Vectors
forceforce——Vectors
angular momentumangularmomentum——Vectors
linear momentumplin——Vectors
electric fieldelectricfield——Vectors
average velocityaveragevelocity——Vectors
magnetic momentmagneticmoment——Vectors
relative velocityvAB——Vectors
impulseimpulse——Vectors
first vectorA—0 … ∞Vectors
second vectorB—0 … ∞Vectors
angle betweenφ—0 … 3.142Vectors
resultantR—0 … ∞Vectors
resultant directionβ—0 … 3.142Vectors
directionα—-3.142 … 3.142Vectors
x componentAx——Vectors
y componentAy——Vectors
A=Ax2+Ay2
magnitude from components
R2=A2+B2+2⋅A⋅B⋅cos⁡φ
law of cosines
R⋅sin⁡β=B⋅sin⁡φ
law of sines
R⋅cos⁡β=A+B⋅cos⁡φ
along the first
Ax=A⋅cos⁡α
resolved along x
Ay=A⋅sin⁡α
resolved along y