Physics of a Top

INTRODUCTION

When you spin a top fast, it has a lot of angular momentum. This makes the top stable. The greater the angular momentum, the longer the top will spin. Like regular momentum, angular momentum can be increased by increasing the mass of the top (especially in certain locations) and by increasing how quickly it is spinning. Friction between the top and the air and the surface on which it is spinning eventually causes the top to slow down and lose its angular momentum. This is when it begins to wobble (precession) and, ultimately, fall over.

RELEVANT TERMINOLOGY

Angular acceleration: How much faster or slower a top is spinning over time. (The change in an object’s angular velocity over time)

Angular momentum: How likely something is to keep spinning. If it’s spinning really fast, it has more angular momentum than if it’s spinning slowly. An object’s angular momentum results from its angular velocity and the way its mass is distributed.

Angular velocity: How many times per second an object spins. A car tire spinning 100 times each minute has twice as much angular velocity as the same tire spinning 50 times per minute.

Gyroscopic effect: When tops are spinning, they resist spinning in a different direction. This is the gyroscopic effect—the tendency of a spinning wheel to resist a change in its orientation. (See video)

Momentum: Momentum is the product of mass and velocity (P=MV). The amount of mass in motion. An object’s momentum depends on how much matter (its mass) is moving and how fast it is moving. A boulder speeding down a mountain has much more momentum than a marble rolling slowly across the floor and would require much more energy to stop it.

Figure Skaters and Spinning Tops

You may wonder why there is a video about a figure skater on a page about the physics of a top; well, they use the same principles. When the skater in the video pulls her arms and legs closer to her body, she spins faster. When her arms or legs are outstretched, she rotates slower due to angular momentum. The angular momentum does not change when she moves her arms. What does change is the rate at which she is spinning due to a change in her rotational mass. When she draws them in, her rotational mass lessens, thus causing her angular velocity to increase, or simply put, she spins faster. So, in summation, having the weight closer to the center increases speed(revolutions per minute or RPMs), while having the weight farther from the center slows velocity. The same holds with a top.

University of Nebraska - Lincoln, Physics of Olympian feats: Spinning figure skater

Anatomy of a Top

A top is made up of three basic elements, the tip or point, the whorl or body, and the spindle or shaft. The top spins on its tip or point. The spindle or shaft is sometimes used to spin the top using one’s fingers. Between the spindle and the tip is the whorl of the top. Tops can be made of many different materials, such as clay, wood, ceramic, or plastic.

Considerations (from Brian Lemin)

  • For speed, keep the bulk of the weight close to the rotational axis.

  • For a greater spin time, keep the bulk of the weight toward the perimeter of the whorl.

  • The heavier the top, the longer it will spin.

  • The greater diameter of the whorl, the longer the top will spin.

  • The greater the diameter, the more stable the top will be.

  • The more weight on the perimeter of the whorl, the more difficult it will be to spin by hand.

  • The more weight you have on the perimeter the more thought you have to put into the design of the spindle. In other words, the more weight, the larger the diameter of the spindle should be or have a section of the spindle larger for spinning. Also, there will be a greater need for some sort of "grip" being built into the design (i.e. knurling).

  • The position of the whorl on the spindle affects the stability and processing of the top.

    • The lower the whorl the more stable.

    • Higher than one-third of the shaft length begins to make the top more difficult to spin. Though palm spin (faster spinning) tops will work OK at above this height.

    • It will still spin, but it spins better if the proportional position is lower than one-third.

  • Whorl and weight principles can be stated more scientifically by talking about the center of gravity, instead of where the majority of the weight is positioned.

  • Design your top shape for aerodynamics.

    • Air friction does have an effect, though only really noticeable on a very "whiskery" top.

  • Reduce friction at the contact point.

    • A sharp, but not penetratingly sharp point will be better than a blunt point.

    • A sharp point is more likely to break or dull over time.

    • Metal is better than most woods as a spinning point.

    • Glass is a great surface to spin a top on. (A concave shaving mirror helps keep the top confined to a small area)

Dig deeper... there is a considerable amount of research and information out there to assist you in the design phase.

Additional Resources