Living on a spinning planet

Spinning at 1000 miles per hour! What?

We are living on a spinning planet. If you live on the equator, then you are moving at about 1000 mph because of the rotation of the Earth. People have asked, "Wouldn't this create extremely high winds?" and "Wouldn't the centrifugal force from such fast spinning throw us off into space?" These are fair questions! Let's use them to learn about a couple of science topics, starting with the wind question.

Bake a cake

If you've spent time baking, you've probably noticed that a liquid in a spinning mixing bowl will acquire the same rotation as the bowl. This video shows the process.

Mixing bowl animation

When the bowl first starts to spin, most of the liquid is not moving. A layer of liquid at the periphery is dragged around by friction between the liquid and the bowl's surface. This layer in turn starts dragging the layer just inside it. This is because there is friction between layers of fluid when one layer slides past another one. This frictional stickiness is called viscosity. The dragging influence spreads inward so that after a time, the liquid in the mixing bowl is all spinning as if it was a solid disk. This video shows a lab demonstration that could be easily reproduced in science classrooms.

Air also has friction with the ground and it has viscosity. The surface of the Earth will tend to drag along the layer of air at the ground, and this air layer will in turn drag along the air layer above it. If we imagine a hypothetical spinning planet with a stationary atmosphere, these frictional forces would over time "spin up" the entire atmosphere. When things settle, the atmosphere would rotate with the planet just as if it was a solid crust. An inhabitant of the planet would experience no wind at all. We can imagine such a "spin up" process by turning the mixing bowl inside out:

Planet spinning up its atmosphere

This animation is an oversimplification of the process. The air flow would initially have a lot of turbulent eddies, and these would over time settle into small scale random molecular motions, which is the same as heat. But the end result is the same. The atmosphere would rotate with the Earth.

Of course, we do experience winds, but they are small departures from the solid crust motion I've described. Winds are caused by the nonuniform heating of the Earth by the sun and the resulting temperature differences from place to place. That's a topic for another post!

Centrifugal force: How fast is "fast" spinning?

At minimum, how fast would the Earth need to be spinning at the equator for someone there to be propelled up off the ground by the centrifugal force?

(a) 167 mph

(b) 945 mph

(c) 5452 mph

(d) 17634 mph

(e) 66000 mph

While you ponder this, let's think about something we've experienced. Imagine driving into a leftward curve on a highway at a speed of 60 mph. In the passenger's seat, how much force do you feel pushing you against the car door? We can't answer that question until we know how tight the curve is. The smaller the circle, the larger the force. A gentle curve with a 1-mile radius would give a small force, about 5% of your body weight. A tight curve with a radius of 100 feet would give a force almost two and a half times your body weight. (Physicists, by the way, would say that your body is trying to keep going in a straight line according to Newton's First Law, and the car door is pushing you to the left to make you follow the curve. Our main concern right now is the strength of the effect.)

Centrifugal force then is determined by two factors, and they both have equal say. The first factor is your speed. Pick your favorite units, mph or meters/sec. The second factor is your angular speed around the circle. Again, pick revolutions per minute (rpm), degrees per second, or whatever units you like. This second factor measures the tightness of the curve; the smaller the circle, the more often you go around it. Multiply these two factors and you get a number that measures the strength of the centrifugal force.

Getting back to the spinning Earth, 1000 mph seems fast, but the equator is a very large circle. The angular speed is 1 revolution per day or only about 0.0007 rpm. From space, an observer would need to watch the Earth for a long time to detect any rotation at all. The centrifugal force would be about 1/300th of your body weight. A polar bear cub that normally weighs 300 pounds would experience an upward centrifugal force of about 1 pound at the equator. On a bathroom scale, she would weigh 299 pounds.

A polar bear celebrating his weight during his trip to the tropics

The best answer to the above quiz is (d). The Earth would need to spin at 17634 mph at the equator for the bear to achieve weightlessness, and faster for her to be propelled upward. Not coincidentally, that's close to the velocity needed to maintain low-Earth orbit. One way of understanding how a satellite stays in orbit is that it goes just fast enough for the centrifugal force to support its weight and prevent it from falling to the ground.