The basic physics of spinning tops

by | Spinning Tops

Spinning tops are fascinating to watch. They have amused cultures around the world for centuries. One of the main things we find so intriguing about them is that they appear to defy gravity. The way they move seems counterintuitive. Well-made tops, such as Scovie tops, seem to keep spinning far longer than we feel like they probably should.

The motion of a top can be explained by the physics of spinning.

This article won’t get into the nitty-gritty. I won’t rattle off equations, laws, and the famous scientists they’re named after. This is a high-level summary of the physics of spinning tops – written in plain English – for anyone who has ever been intrigued as they watch a top spin.

How science sees a spinning top

The movement of a spinning top is more complex than many people realize. A top doesn’t simply spin. It rotates, precesses, reorients, and is affected by external forces.

In physics, a top is what is known as a rigid body. When a rigid body is fixed at a single point, there is 3 degrees of freedom for its motion. A spinning top in motion:

  1. Rotates around its own axis (ie, the spin)
  2. Tilts to the side
  3. Rotates around a vertical z-axis

Numbers 2 and 3 may not be noticeable until the top starts slowing down. A balanced top given a forceful spin on a hard surface spins exactly vertically at first – at least to the naked eye.

A fundamental property of a rigid body is the moment of inertia. This is a measure of the resistance to rotation about the top’s axis. It determines the torque required for a change in angular velocity. Tops with maximal moment of inertia have most of their mass concentrated on the outer edge. This explains why tops have a wide portion.

The physics of spinning a top for long-lasting motion

When not moving, most of a top’s weight rests as low to the ground as possible. If you let go of a top without spinning it, it will topple to the side until its wide part comes to rest on the surface. We’re used to this effect of gravity in all aspects of our lives:  objects fall until their center of mass reaches the Earth, unless there is something in the way.

A top will keep falling and repositioning until Its center of mass can’t get any lower. The goal of spinning a top is to counteract this tendency for as long as possible.

When you spin a top, you start by holding the top vertically. This means that you are lifting up its center of mass off of the surface. Then, by giving it a good, hard spin, you create torque and angular velocity.

Then it keeps spinning for a while on its own.

Why a top keeps spinning

As mentioned above, spinning a top provides it with angular velocity about its axis. It also has angular momentum. Whereas linear momentum keeps something moving in a line, angular momentum keeps something spinning.

All moving objects have momentum. The momentum depends on the object’s mass and its velocity. A heavier object has more momentum than a lighter object, and an object moving at a higher speed has more momentum than an object moving at a slower speed. For a top, the faster it spins and heavier it is, the more angular momentum it has.

You’re probably familiar with the phrase “an object in motion stays in motion.” This means that, in the absence of external forces, momentum is conserved and an object will keep moving with the same velocity.

If the energy doesn’t dissipate, the top doesn’t stop spinning. Energy dissipates slowly when a well-balanced top is spinning on a smooth surface. It does dissipate eventually, though, and every top must stop spinning. Keep reading to find out why.

 …and why tops slow down

All moving objects are subject to external forces. How a moving object responds to these external forces depends on what is known as dynamics. Imperfections in the surface that a top is spinning on and imperfections in the top itself further allow these external forces to take effect.

A top begins to slow down because of frictional forces. There is friction between the top’s tip and the surface it is spinning on. To a lesser extent, there is friction between the top and the air around it.

The impact of both of these frictional forces increase if the top starts to wobble. Wobbling results in the tip being dragged across the surface and the body of the top having more contact with the air around it.

Friction can be reduced by decreasing the amount of contact between the top’s tip and the surface. This could be done by using a pointed tip rather than a rounded tip, for example. However, this adjustment comes at a cost. A pointed tip is less sturdy and is more likely to slip on the surface, thereby increasing the effects of friction. A pointed tip is also more likely to become deformed with use over time. This results in wobbling which, as already noted, increases the effects of friction.

Moreover, wobbling causes the vertical axis of the top to tilt to the side. That’s when gravity starts to do damage. Gravitational torque is due to gravity pulling downward on the top’s center of mass. From here, falling over is inevitable. But the top’s angular momentum prolongs this process, creating the long, yet dramatic, ending that we all love to watch.

How a top falls

As a spinning top slows and gravitational torque comes into play, the top’s angular momentum decreases. When it loses enough angular momentum, it falls.

The decrease in angular momentum creates a phenomenon known as precession. This is a change in the orientation of a spinning object, causing it to spin around a secondary axis. With spinning tops, this is seen when the top starts to tilt to the side and there is circular rotation of the top’s axis. Said another way, the axis of rotation precesses in a circle while the top itself is spinning about its own axis.

This is not unlike the Earth’s orbit:  the Earth orbits around the sun (with one revolution taking a year) while simultaneously spinning around its own axis (with one revolution taking a day).

Tilted slightly to one side, the edge of the top is pulled down toward to the ground by gravity, moving closer and closer and time passes. The top begins to precess faster in an attempt to conserve angular momentum.

The precession demonstrated by ultra-tall spinning tops is extremely cool to watch. Check out Scovie’s tall top video on YouTube. (And please subscribe to the channel while you’re there!)

Once a spinning top tilts so much that finally hits the surface, the friction forces that were previously minor suddenly become so major that the top stops spinning almost immediately. The remainder of its movement is a back-and-forth gliding motion until it finally comes to rest.

See the physics of spinning for yourself

The best way to fully appreciate the physics of spinning tops is to see it in action. Get your own top and watch it spin. Learn how to set it into motion effectively. And see how it moves as it slows down and eventually falls over.

The physics of spinning comes into play with any object that is spun. It doesn’t need to be designed for spinning and doesn’t even need to be round. Here a few examples:

  • You can spin a jar lid on its edge and then watch it precess after it falls over.
  • The infamous party game “spin the bottle” only works because of the frictional forces that make the bottle stop spinning.
  • Try twirling an egg and watch it wobble as the liquid inside moves around.

Ready to see the physics of spinning first hand? Get a beautifully precision-machined spinning top from the Scovie Precision Turning store today.

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