Radians in an Arc

Q. An arc 0.5 m long is cut from a circle of radius 2 m. What angle does it make at the centre, in radians? expects 0.25

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.

Check an answer

Q. An arc 0.5 m $s = 0.5$ m long is cut from a circle of radius 2 m $r = 2$ m. What angle does it make at the centre, in radians?

The playground

Inputs

arc

s

0.50 m

radius

r

2.00 m

Outputs

angle

θ

The solution

Solved with Units

Given

$s = 0.5$ m
$r = 2$ m

Find $θ$ .

Working

arc over radius $θ = \frac{s}{r}$
$θ = \frac{0.5}{2}$
$θ = 0.25$

Conclusion

Metres over metres leave a pure number: the radian has no dimensions.

The Ruby

1require_relative "../physics"23question :radians_in_an_arc do4  kind :numerical5  describes "An arc %{arc} long is cut from a circle of radius %{radius}. %{angle}, in radians?"6  given arc: "0.5 m"7  given radius: "2 m"8  asks angle: "What angle does it make at the centre"9end

1require_relative "../questions/radians_in_an_arc"2require_relative "../science/units_and_measurement/units"34solve :radians_in_an_arc, using: Units do5  take arc: :s, radius: :r6  take angle: :theta7  answer find_value(:angle)89  conclusion "Metres over metres leave a pure number: the radian has no dimensions."10end

1require_relative "../solutions/radians_in_an_arc"23play_with :radians_in_an_arc do4  title "Radians in an Arc"5end

The laws

quantity	written	units	within	from
speed of light	$c$	m/s	—	Units
avogadro constant	$N_{A}$	mol⁻¹	—	Units
length	$l$	m	0 … ∞	Units
mass	$m$	kg	—	Units
time	$t$	s	0 … ∞	Units
electric current	$I$	A	—	Units
temperature	$T$	K	—	Units
amount of substance	$n$	mol	—	Units
luminous intensity	$I_{v}$	cd	—	Units
arc length	$s$	m	—	Units
radius	$r$	m	0 … ∞	Units
plane angle	$θ$	—	—	Units
area	$A$	m²	—	Units
solid angle	$Ω$	—	—	Units
light time	$t_{light}$	s	—	Units
light distance	$d_{light}$	m	—	Units
number of entities	$N$	—	—	Units
baseline	$B$	m	—	Units
distance away	$D$	m	—	Units
parallax angle	$θ_{p}$	—	—	Units

θ = \frac{s}{r}

arc over radius

Ω = \frac{A}{r^{2}}

area over radius squared

d_{light} = c \cdot t_{light}

distance at light speed

N = n \cdot N_{A}

entities in moles

θ_{p} = \frac{B}{D}

baseline over distance