moment of inertia of a circle at its edge

For example, it will be much easier to accelerate a merry-go-round full of children if they stand close to its axis than if they all stand at the outer edge.

The moment of inertia depends not only on the mass of an object, but also on its distribution of mass relative to the axis around which it rotates. The basic relationship between moment of inertia and angular acceleration is that the larger the moment of inertia, the smaller is the angular acceleration. Furthermore, the more massive a merry-go-round, the slower it accelerates for the same torque. For example, the harder a child pushes on a merry-go-round, the faster it accelerates. This equation is actually valid for any torque, applied to any object, relative to any axis.Īs we might expect, the larger the torque is, the larger the angular acceleration is. To develop the precise relationship among force, mass, radius, and angular acceleration, consider what happens if we exert a force is the rotational analog to Newton’s second law and is very generally applicable. If you push on a spoke closer to the axle, the angular acceleration will be smaller. The more massive the wheel, the smaller the angular acceleration. The greater the force, the greater the angular acceleration produced. Force is required to spin the bike wheel. There are, in fact, precise rotational analogs to both force and mass. These relationships should seem very similar to the familiar relationships among force, mass, and acceleration embodied in Newton’s second law of motion. The first example implies that the farther the force is applied from the pivot, the greater the angular acceleration another implication is that angular acceleration is inversely proportional to mass. Furthermore, we know that the more massive the door, the more slowly it opens.

For example, we know that a door opens slowly if we push too close to its hinges.

In fact, your intuition is reliable in predicting many of the factors that are involved. If you have ever spun a bike wheel or pushed a merry-go-round, you know that force is needed to change angular velocity as seen in Figure 1.

Study the analogy between force and torque, mass and moment of inertia, and linear acceleration and angular acceleration.

Understand the relationship between force, mass and acceleration.

Moment of inertia of a circle at its edge