Angular Momentum, moment of inertia & Rotational motion

In this post, we will discuss a couple of interesting questions related to Angular Momentum, Torque, moment of inertia & Rotational motion.

How does angular momentum work in rotational motion?

The angular momentum of a rotating object is equal to the product of its moment of inertia and its angular velocity. If there is no external torque on the object, then its angular momentum remains constant.

If there is no external force on an object with linear momentum, then as the object can’t change its mass, its velocity also remains constant. But a rotating object can change its moment of inertia, so, even without external torques, its rotational speed can be changed.

Does momentum apply to objects that rotate?

Just by the term Momentum, we understand linear momentum. Momentum or linear momentum applies to objects moving from one location to another. Since such motion is typically described in straight lines, physicists sometimes call this linear momentum.

In rotational motion objects (such as a spinning top) or systems of objects (such as planets in a solar system) rotate around a central point or axis.

In rotational motion, we have a separate set of physical quantities that are similar or equivalent to the physical quantities that describe linear motion.

Position in linear motion is replaced by angle; velocity is replaced by angular velocity; acceleration is replaced by angular acceleration, and force is replaced by torque. [ See this: linear motion & rotational motion equivalents and relationships]

The rotational analog to momentum is called angular momentum, and in any system of objects, in the absence of external torques, the angular momentum in the system is conserved.

Hence, we can say that angular momentum applies to objects that rotate.

How does torque take the place of force when measuring rotational motion?

All of us should have had a common experience that illustrates how torque works.

Suppose we want to push open a door that rotates about its hinges. We know that the speed with which the door opens depends on how hard we push. This push is the force we apply. Speed of opening of the door also depends on how far from the hinges we push—the farther, the faster.

It also depends on the angle at which we push. Pushing at a right angle to the door is much more effective than pushing at a smaller or larger angle. If we push at a right angle, then torque equals the force times the distance from the axis of rotation.

What takes the place of mass when measuring rotational motion?

Mass is defined as the net force on an object divided by its acceleration. By analogy, then, the property that takes the place of mass should be the torque divided by angular acceleration. The property is called rotational inertia or the moment of inertia.

It depends not only on mass but on how far the mass is from the axis of rotation. The further the mass is from the axis, the larger the moment of inertia.

If we sit on a rotating chair while holding heavy weights, the further we extend our arms, the more becomes the moment of inertia. That means the more difficult it is for someone to start us rotating. That is the concept of inertial in rotation and we call it the moment of inertia.

That is, it will require more torque to achieve the same angular acceleration when the moment of inertia is more.

Angular Momentum, moment of inertia & Rotational motion
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