Interactive physics simulator
Earth's Rotation — Spin, Day & Night & the Coriolis Effect
Watch Earth spin in real time on its tilted axis, see the day-night terminator sweep across continents, visualise the Coriolis deflection of air masses, and inspect live angular & linear velocity data — all computed from real orbital mechanics.
Earth's Rotation & Day–Night Cycle Simulator
Drag the speed slider to fast-forward time. Use tabs to switch views. Toggle axis, grid, and Coriolis arrows.
Live Rotation Data
- Angular Velocity
- 7.27 × 10⁻⁵ rad/s
- Equatorial Speed
- 463 m/s
- Rotation Angle
- 0°
- Day Progress
- 0%
- UTC Time
- 00:00
- Axial Tilt
- 23.5°
- Sidereal Day
- 23h 56m
- Solar Day
- 24h 00m
What is Earth's Rotation?
Earth's rotation is the spinning of Earth on its own axis — an imaginary line passing through the North and South Poles. Earth completes one full rotation every 24 hours (solar day), creating the cycle of day and night.
Earth rotates west to east (counterclockwise viewed from above the North Pole), which is why the Sun appears to rise in the east and set in the west.
- Angular velocity: ω = 7.27 × 10⁻⁵ rad/s
- Equatorial linear speed: ≈ 1,670 km/h (463 m/s)
- Axial tilt: 23.5° to the ecliptic plane
- Sidereal day: 23 h 56 min 4 s (relative to stars)
- Solar day: 24 hours (relative to the Sun)
Key Formulas
ω = 2π / T ω = angular velocity (rad/s), T = period (s). For Earth: T = 86,400 s → ω ≈ 7.27 × 10⁻⁵ rad/s
v = ω × R × cos(φ) v = linear speed (m/s), R = Earth radius (6.371 × 10⁶ m), φ = latitude
a = ω² × R × cos(φ) Due to rotation, surface points experience centripetal acceleration directed toward Earth's axis
a_C = 2v × ω × sin(φ) v = object speed, ω = Earth's angular velocity, φ = latitude. Maximum at poles, zero at equator.
T_solar = T_sid × (1 + T_sid/T_yr) T_sid ≈ 86,164 s (sidereal), T_yr ≈ 365.25 days. The extra 3 min 56 s compensates for Earth's orbital movement.
Effects of Earth's Rotation
Earth's rotation produces several major physical effects:
| Effect | Cause | Example |
|---|---|---|
| Day & Night | One side faces Sun, other faces away | 24-hour cycle of light and dark |
| Coriolis Effect | Rotating reference frame deflects moving objects | Cyclones spin clockwise (SH) or CCW (NH) |
| Equatorial Bulge | Centrifugal effect pushes mass outward | Earth is 21 km wider at equator than poles |
| Time Zones | 360° / 24h = 15° per hour of longitude | 24 time zones, each ~1 hour apart |
| Tidal Braking | Moon's gravity slows Earth's spin | Days gradually get longer (~1.4 ms/century) |
| Trade Winds | Coriolis deflects air from high to low pressure | Northeast trade winds between 0°–30°N |
Solved Examples
Calculate Earth's angular velocity of rotation.
- Earth completes one full rotation (2π radians) in 24 hours = 86,400 s
- ω = 2π / T = 2π / 86,400
- ω = 6.2832 / 86,400
Answer: ω ≈ 7.27 × 10⁻⁵ rad/s
Find the linear speed of a person standing at the equator.
- Earth radius at equator: R = 6.371 × 10⁶ m
- v = ω × R = 7.27 × 10⁻⁵ × 6.371 × 10⁶
- v = 463 m/s
Answer: v ≈ 463 m/s ≈ 1,670 km/h
At 45° latitude, what is the linear speed of rotation?
- Radius at latitude φ = 45°: r = R·cos(45°) = 6.371 × 10⁶ × 0.7071
- r = 4.505 × 10⁶ m
- v = ω × r = 7.27 × 10⁻⁵ × 4.505 × 10⁶
Answer: v ≈ 327 m/s ≈ 1,180 km/h
Common Mistakes
- Confusing rotation (spinning on own axis) with revolution (orbiting the Sun).
- Thinking the Sun moves — actually Earth's rotation creates the apparent motion of the Sun across the sky.
- Assuming linear speed is the same everywhere — it depends on latitude: v = ωR cos(φ). At poles, v = 0.
- Confusing sidereal day (23h 56m) with solar day (24h) — they differ by ~4 minutes due to Earth's orbital motion.
- Thinking the Coriolis effect makes water drain clockwise or counterclockwise in sinks — at sink scale the effect is too small; it only matters at large scales (weather systems).
Practice Questions
1. What is the period of Earth's rotation and what does it define?
Earth completes one rotation in approximately 23 hours 56 minutes 4 seconds (sidereal day) relative to distant stars, or 24 hours (solar day) relative to the Sun. This period defines the length of one day.
2. Why does the Sun appear to rise in the east and set in the west?
Earth rotates west-to-east (counterclockwise when viewed from the North Pole). Because of this, the Sun appears to move in the opposite direction — rising in the east and setting in the west.
3. A person stands at latitude 60°N. Calculate their linear rotation speed.
r = R·cos(60°) = 6.371×10⁶ × 0.5 = 3.186×10⁶ m. v = ω·r = 7.27×10⁻⁵ × 3.186×10⁶ ≈ 232 m/s.
4. What would happen if Earth stopped rotating?
If Earth stopped rotating: (1) One hemisphere would face the Sun permanently — extreme heat on one side, permanent night on the other. (2) The equatorial bulge would collapse over geologic time. (3) The Coriolis effect would vanish, altering wind patterns, ocean currents, and weather systems. (4) Tidal locking to the Sun would eventually occur.
5. How does Earth's rotation create the Coriolis effect?
Because Earth rotates, any freely moving object (air, water, projectiles) is deflected to the right in the Northern Hemisphere and to the left in the Southern Hemisphere, due to the rotating reference frame. This deflection is the Coriolis effect, which drives cyclone rotation directions and trade wind patterns.
Frequently Asked Questions
How fast does Earth rotate?
Earth completes one full rotation every 24 hours (solar day). At the equator, the surface moves at about 1,670 km/h (463 m/s). At the poles, the linear speed is effectively zero, though the angular speed is the same everywhere.
In which direction does Earth rotate?
Earth rotates west to east — counterclockwise as viewed from above the North Pole. This is called prograde rotation and is shared by most planets in the Solar System.
What causes day and night?
As Earth rotates on its axis, different parts of the surface face the Sun (daytime) or face away from the Sun (nighttime). One complete rotation takes 24 hours, producing a full day-night cycle.
What is the difference between a sidereal day and a solar day?
A sidereal day (23h 56m 4s) is Earth's rotation period relative to distant stars. A solar day (24h) is relative to the Sun, and is slightly longer because Earth has also moved along its orbit, so the Sun must travel a little extra to appear at the same position in the sky.
What is Earth's axial tilt and why does it matter?
Earth's axis is tilted at 23.5° to its orbital plane (ecliptic). This tilt causes the seasons: as Earth orbits the Sun, one hemisphere receives more direct sunlight (summer) and the other receives less (winter).
Does Earth's rotation speed change?
Yes. Earth's rotation is very gradually slowing due to tidal braking from the Moon. Days were shorter billions of years ago (≈21 hours 1.4 billion years ago). Earthquakes and the redistribution of mass can also cause tiny speed changes.
What is the Coriolis effect?
The Coriolis effect is a deflection of moving objects (air masses, water, projectiles) in a rotating reference frame. In the Northern Hemisphere objects deflect right; in the Southern Hemisphere they deflect left. It drives trade winds, ocean gyres, and the rotation direction of hurricanes.
What is the equatorial bulge?
Earth bulges slightly at the equator (radius 6,378 km) compared to the poles (6,357 km) because centrifugal effects from rotation push mass outward. Earth is therefore an oblate spheroid, not a perfect sphere.
What would happen to time zones without Earth's rotation?
Time zones exist because different longitudes receive sunlight at different times due to Earth's rotation. Without rotation, there would be a single permanent day side and night side, making the concept of time zones meaningless.
How does rotation create the bulge at the equator?
The centrifugal effect of rotation acts outward, perpendicular to the axis. At the equator this effect is maximum, causing material to bulge outward by about 21 km compared to the poles, giving Earth its oblate spheroid shape.
Why don't we feel Earth spinning?
Earth's rotation is so slow (one revolution per day) and so uniform that we cannot sense it through our vestibular system. The rotation speed is nearly constant, so there is no noticeable acceleration — similar to how you don't feel a smooth airplane flight at constant speed.
What is the relationship between angular and linear velocity in Earth's rotation?
At any latitude φ, the linear speed v = ω × R × cos(φ), where ω ≈ 7.27 × 10⁻⁵ rad/s and R = 6.371 × 10⁶ m. Linear speed is maximum at the equator (φ = 0°) and zero at the poles (φ = 90°). Angular speed ω is identical everywhere.