## Concept explanation A **simple pendulum** is a mass hanging from a fixed point that moves back and forth under gravity. Even when you change the **starting angle** so the motion becomes wider or narrower, the bob still swings within one **vertical plane**. A larger starting angle gives the pendulum a bigger arc and, in this visualisation, a visibly slower back-and-forth rhythm, but the motion never twists out of that flat plane. ## What you see You are looking at a pendulum suspended from a fixed pivot near the top of the canvas. The blue bob moves side to side while the faint guide lines and dashed baseline mark the boundaries of its swing plane. The curved teal arc shows the full range set by the current starting angle, helping you compare how the width of the swing changes while the motion remains confined to the same flat slice of space. ## Try it yourself - **Move the starting-angle slider** to a small value like `10°` and notice how the bob stays close to the centre. - **Increase the slider** toward `60°` and watch the swing become wider while still staying in the same plane. - **Compare the timing** at small and large angles to see that the larger swing moves more slowly in this model. - **Focus on the guide lines** and notice that the bob always travels back and forth between them rather than moving toward or away from you. ## Concept explanation An ideal **pendulum** swings back and forth in a single **swing plane** set by how it was started. If no outside twisting force acts on it, that plane stays fixed relative to space, even if you change your viewpoint. The pendulum is not “deciding” to turn toward a new compass direction on its own; instead, a rotating observer can make the motion *look* different while the underlying direction remains the same. ## What you see You are looking at the pendulum either from above or from the side. In the top view, the bob moves along one straight blue line through the center, while the outer **compass frame** and star field give you a stable reference. In the side view, you see the same motion as a projection from a different viewing angle, and the rotation badge shows how much the camera has been turned. ## Try it yourself - **Press `Rotate Camera 30°`** several times and notice that the swing line keeps the same alignment relative to the fixed stars and compass. - **Switch to side view** and compare how the same pendulum motion looks when you change viewpoint instead of changing the pendulum itself. - **Adjust the swing direction slider** to choose a new initial plane, then **rotate the camera again** to see that the plane stays fixed after you set it. - **Change the amplitude** to make the bob travel farther or less far along the same line. - **Adjust the speed slider** to slow down or speed up the oscillation while the direction remains unchanged. - **Toggle the stars checkbox** to compare the motion with and without a fixed background reference. ## Concept explanation A **Foucault pendulum** shows Earth’s rotation because its **swing plane** tends to stay nearly fixed in space while the **ground reference frame** turns underneath it. From above, that makes the pendulum seem to rotate relative to the floor markings, even though the line of motion is not being actively twisted by a hidden force. The apparent turning depends on **latitude**: at the equator the floor gives almost no apparent turning, while closer to the poles the floor rotates more strongly beneath the fixed swing plane. ## What you see You’re looking down on a circular floor marked with compass directions. The blue line is the pendulum’s swing plane, held fixed to represent the nearly constant direction in inertial space, while the floor and its `N`, `E`, `S`, `W` markings rotate beneath it. The teal arc measures the **apparent angle** between the swing line and the rotating floor, so you can watch that angle change and connect the effect to Earth’s rotating frame rather than to the pendulum itself turning. ## Try it yourself - **Drag the play speed slider** to make the floor rotate faster or slower, and watch how the angle to the compass markings changes even though the blue swing line stays put. - **Move the latitude slider** toward `0°` and notice how the apparent turning fades, then **push it toward `90°`** to see the floor sweep beneath the line more strongly. - **Compare the blue line to the `N` mark** as time passes, and notice that the changing direction is really the floor moving under a nearly fixed plane. - **Press Reset view** to return to the starting orientation and replay the effect from the same reference frame. - **Pause mentally on the pivot point** and ask: is the line rotating, or is the Earth-marked floor rotating underneath it? ## Concept explanation A **Foucault pendulum** swings in nearly the same plane in space, but because Earth rotates beneath it, an Earth-bound observer sees that swing direction slowly turn. This apparent turning is called **precession**. The rate depends on **latitude**: at the pole the swing plane appears to rotate fastest, while at the equator it does not rotate at all. In this view, you are seeing the pattern traced on the observatory floor from the observer’s frame on Earth. ## What you see The circular floor acts like an observatory dial, with degree markings around the edge. Each thin colored line is a past swing path, so as time advances the trace gradually fans around the circle and reveals the precession pattern. The bright teal line shows the pendulum’s current swing direction, and the moving bob marks the pendulum’s position along that line at the present moment. ## Try it yourself - **Drag the time slider** slowly from `0 h` to later times and watch the floor trace build up one swing direction after another. - **Pause at `12 h` and `24 h`** to compare how far the swing direction has rotated for an observer standing on Earth. - **Adjust the latitude slider** toward `0°` and notice how the precession nearly disappears. - **Move the latitude slider** toward `90°` and see the trace rotate much more quickly over the same number of hours. - **Press the reset button** to return to the starting state and replay the buildup from the beginning. ## Concept explanation A **Foucault pendulum** keeps swinging in nearly the same plane in space while Earth rotates underneath it. Because of that, the swing direction appears to turn relative to the floor; this turning is called **precession**. The rate depends on **latitude**: at the **poles**, the floor spins fully beneath the pendulum so the apparent turning is fastest, while at the **equator** there is no apparent turning at all. In between, the rate scales with `sin(latitude)`, so moving farther from the equator makes the precession stronger. ## What you see You can compare two linked views. On the left, a marker shows where the pendulum sits on the globe. On the right, the circular floor diagram shows the pendulum’s swing trace and how quickly that trace rotates at the chosen location. The speed bar and direction readout update as you move between hemispheres, so you can see both how fast the trace turns and whether it turns clockwise or counterclockwise. ## Try it yourself - **Drag the marker** toward the equator and notice how the trace rotation slows until it nearly stops. - **Move the latitude slider** toward `90°N` or `90°S` and watch the speed bar rise toward the pole rate. - **Cross the equator** and see the turning direction reverse between clockwise and counterclockwise. - **Toggle animate trace** off to pause the motion, then **reset trace** to compare different latitudes from the same starting angle. - **Compare equal north and south latitudes** such as `45°N` and `45°S` to see that the speed matches while the direction flips. ## Concept explanation A **Foucault pendulum** appears to rotate its swing direction because Earth is turning beneath it. The apparent rotation rate, called **precession**, depends on **latitude**: at the **equator** the floor does not rotate relative to the swing plane at all, at a **mid-latitude** it rotates more slowly, and at the **pole** it completes the full effect most strongly. Comparing all three at the same shared time makes the pattern easy to see: higher latitude means faster apparent precession. ## What you see You are looking at three floor-view pendulum diagrams side by side. Each panel shows the current swing line, a moving bob, and a short trail of recent motion. The left panel is fixed at the equator, the middle panel uses a selectable mid-latitude, and the right panel shows the pole. Because all three update together from one shared clock, you can directly compare how much each swing plane has rotated by the same moment in time. ## Try it yourself - **Press Play/Pause** to stop the shared clock and inspect one moment across all three diagrams. - **Drag the time slider** forward and backward to compare the equator, mid-latitude, and pole at exactly the same time. - **Change the mid-latitude dropdown** from `30°` to `45°` to `60°` and notice how the middle diagram’s precession rate increases. - **Watch the equator panel** and notice that its swing line keeps the same orientation while the others rotate. - **Compare the pole panel** against the middle panel and see that the pole accumulates the largest angular change over the same interval. - **Press Reset** to return all three diagrams to the same starting orientation and replay the comparison. ## Concept explanation A **Foucault pendulum** gives visible evidence that **Earth rotates** because its swing plane stays nearly fixed in inertial space while the local **floor frame** slowly turns with Earth. That means the pendulum is not really twisting itself around the room; instead, the room, the observer, and the floor’s direction are gradually rotating underneath it. The rate of that change depends on latitude, which is why the angle relative to the room changes faster closer to the poles and not at all at the equator. ## What you see You are looking at one idea from three linked viewpoints. The large panel shows the pendulum above the room floor, with a teal dashed line marking the nearly space-fixed swing plane and a gold room axis showing the room’s current direction. The Earth inset shows the floor direction rotating on a small Earth patch, and the observer panel shows how a person standing on the floor experiences that same change. The angle readout updates to show the pendulum’s swing direction measured relative to the room. ## Try it yourself - **Switch the reference frame** between `Earth-fixed view` and `Space-fixed view` to compare what stays still and what rotates. - **Scrub the time slider** and watch the gold room axis turn while the teal swing plane stays fixed in space. - **Pause the animation** and **step through time slowly** to see that the measured angle changes even though the pendulum’s space direction does not. - **Adjust the latitude slider** toward `0°` and notice the room-relative angle changes more slowly. - **Move the latitude slider** toward `90°` and see the room frame rotate faster beneath the same swing plane. - **Reset the scene** and then **compare the angle readout** in both views to connect the visuals with the measurement.