SME
Physical Geology
Plate tectonics
Use this for “A plate turns 0.5° per million years. How fast does a point 60° from its pole move?”
Diagram
The plate turns 0.5° = 0.00873 rad per million years about its Euler pole.
A point Δ = 60° away moves v = ω × 6,371 km × sin Δ = 48.1 mm/yr (1 km per Myr is 1 mm per year).
Speed grows with sin Δ: 0 at the pole, 55.6 mm/yr at 90° (the dotted arrow).
This is an example. Type your own values to start a new problem.
ωrad (rad/Myr)
=
ω (°/Myr)
×
π
÷
180
v (mm/yr)
=
ωrad (rad/Myr)
×
R
×
sin(
Δ
°)
Formulas
ωrad
=
ω
×
π
180
0.008727
=
0.5
×
π
180
v
=
ωrad
×
6,371
×
sin(
Δ
°)
48.1488 = 0.008727 × 6,371 × sin(60°)
Assumptions
•
A plate turns as a rigid cap about its Euler pole; Earth’s radius R = 6,371 km.
•
Speed is greatest 90° from the pole and 0 at it: v = ωR sin Δ, with ω in radians.
•
1 km per million years is 1 mm per year, so km/Myr reads straight as mm/yr.
Step-by-step
WE KNOW
ω = 0.5 °/Myr, Δ = 60°
FIND
rotation rate in radians (ωrad), speed (v)
Step 1 · Find rotation rate in radians (ωrad)
Use ωrad = ω × π ÷ 180
Degrees
to
radians:
times
π
180
.
ωrad
=
0.5
×
π
180
ωrad = 0.00872665 rad/Myr
Step 2 · Find speed (v)
Use v = ωrad × 6,371 × sin(Δ°)
The
point
circles
the
pole’s
axis
at
radius
R
sin
Δ
,
so
its
speed
is
ω
(in
radians)
times
that
radius.
v
=
0.00872665
×
6,371
×
sin(60°)
sin(60°) = 0.866
6,371 × 0.866 = 5,517 km, the circle’s radius
v
=
0.008727
×
5,517
v
=
48.1488
mm/yr
Check
Put the numbers back in. Both sides should match.
0.00872665
=
0.5
×
π
180
✓
48.1488 = 0.00872665 × 6,371 × sin(60°) ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.