What is the law of motion of a fidget spinner?

The motion of a fidget spinner can be explained through the principles of rotational dynamics and conservation of angular momentum. Here's a breakdown of the key laws and concepts that govern the motion of a fidget spinner:

1. Newton's First Law of Motion (Inertia)

Newton's First Law states that an object will remain at rest or in uniform motion unless acted upon by an external force. For a fidget spinner, this means:

• When you spin the fidget spinner, it will continue to rotate in the absence of any external forces (like friction or air resistance) acting on it.
• The fidget spinner resists changes in its state of motion due to its inertia. If it is spinning, it will continue spinning unless acted on by forces that slow it down.

2. Conservation of Angular Momentum

Angular momentum is a measure of an object's rotational motion and depends on its moment of inertia and angular velocity. The law of conservation of angular momentum states that if no external torque (twisting force) is applied, the angular momentum of an object remains constant.

For a fidget spinner:

• Once you give it an initial spin, the fidget spinner will maintain its rotational motion for a while because of the conservation of angular momentum.
• The spinner’s angular momentum is conserved as long as there are no significant external forces (other than friction and air resistance) acting to stop the motion.

3. Rotational Kinetic Energy

When a fidget spinner is spinning, it possesses rotational kinetic energy. This energy depends on its moment of inertia (how mass is distributed relative to the axis of rotation) and the angular velocity (how fast it spins).

• The moment of inertia for a fidget spinner depends on factors like its shape, mass, and the distribution of its mass.
• As the spinner spins, it loses some of this energy due to friction at the contact points (between the spinner and the surface it's placed on), as well as air resistance, which slowly converts the spinner's rotational kinetic energy into heat.

4. Torque and Angular Acceleration

The motion of the fidget spinner is initiated by applying a force (torque) to its central axis, usually by flicking it with a finger.

• Torque (τ) is the force that causes the spinner to rotate. It is defined as the force applied multiplied by the distance from the center of rotation (the radius).

  $$\tau = F \times r$$

  where $F$ is the force applied and $r$ is the radius from the center of the spinner to the point of application of force.

• The application of torque causes angular acceleration (how quickly the rotational speed changes), which increases the spinner’s angular velocity.

5. Friction and Damping

• Friction is the force that resists the motion of the spinner. There are two primary types of friction at work:
  • Bearing friction: In most fidget spinners, there are bearings at the center that help reduce friction. However, these bearings still cause some resistance that slows down the spinner over time.
  • Air resistance: As the spinner moves, the air around it exerts a drag force that also slows it down.
• The combined effect of friction and air resistance eventually leads to a decrease in the spinner’s angular velocity, causing it to come to a stop.

6. Precession (In Some Cases)

If a fidget spinner is not perfectly balanced, you might notice it exhibiting precession, a phenomenon where the axis of rotation of the spinner slowly moves or tilts in a circular direction. This happens because of the torque caused by the force of gravity acting on the mass of the spinner, especially if the spinner is tilted.

Precession occurs because the forces acting on the spinner (gravitational force, friction) can cause the orientation of the axis of rotation to change slightly as it spins. However, this effect is usually very subtle in most fidget spinners.

Summary of Motion Laws for a Fidget Spinner

1. Inertia (Newton's First Law): The spinner will continue spinning unless acted on by an external force (like friction).
2. Conservation of Angular Momentum: The spinner's rotation will continue at a constant speed unless friction or other external forces interfere.
3. Rotational Kinetic Energy: The spinner has rotational energy that decreases due to friction and air resistance, slowing it down over time.
4. Torque and Angular Acceleration: The motion starts when torque is applied, causing the spinner to accelerate rotationally.
5. Friction and Damping: Friction gradually slows down the spinner and causes it to eventually stop.
6. Precession: If the spinner is unbalanced, its rotational axis can shift slightly due to external forces like gravity, creating precession.

These laws combine to explain the behavior of a fidget spinner, from its initial spin to the gradual slowing and eventual stopping of the motion.