When you take an object and spin it faster and faster, its linear speed does increase. This effect is due to the conservation of angular momentum. Let's break down what happens:
Angular Speed: When you spin an object, it has an angular speed, which represents how fast it rotates around a fixed axis. Angular speed is usually measured in radians per second (rad/s).
Angular Momentum: The angular momentum of the spinning object is the product of its moment of inertia and its angular speed. The moment of inertia depends on the distribution of mass in the object and how far that mass is from the axis of rotation.
Conservation of Angular Momentum: According to the conservation of angular momentum, the total angular momentum of a system remains constant if no external torques act on it. In other words, if no external forces are applied to the object to change its rotation, the product of its moment of inertia and angular speed will remain the same.
Now, when you increase the angular speed of the spinning object, its moment of inertia will usually remain constant (assuming the mass and shape don't change). As a result, to conserve angular momentum, the angular speed must increase.
The relationship between angular speed and linear speed is given by the formula:
Linear Speed (v) = Angular Speed (ω) × Radius (r)
As the angular speed increases, the linear speed also increases, provided that the radius remains the same. For example, think of a figure skater spinning on ice. When they pull their arms closer to their body, they decrease their moment of inertia, and to conserve angular momentum, their angular speed increases, causing them to spin faster. This phenomenon is known as the "conservation of angular momentum."
It's important to note that there are practical limits to how fast an object can spin before it undergoes structural deformation or failure due to the centrifugal forces acting on it.