Objects undergo rotation when a torque, or rotational force, is applied, often as a result of an external influence.

In physics, rotation is defined as the movement that occurs when a force is exerted at a distance from an object’s center of mass, rather than directly at it. This force is referred to as torque. Torque, sometimes called the moment of force, serves as the rotational equivalent of linear force. It is mathematically expressed as the product of the applied force and the distance from the point of rotation to the point where the force is applied:

where $\tau$ represents torque, $F$ is the magnitude of the applied force, and $r$ is the distance from the axis of rotation (also known as the moment arm or lever arm).

The direction of rotation is determined by a principle known as the right-hand rule. To apply this rule, curl the fingers of your right hand in the direction of the applied force; your thumb will then point in the direction of the resulting rotation.

The extent of rotation is influenced by several factors: the magnitude of the force, the length of the moment arm, and the angle at which the force is applied. A greater force or a longer moment arm results in increased torque, which in turn leads to greater rotation. Additionally, if the force is applied at a larger angle relative to the lever arm, the torque will also be enhanced, producing a larger rotational effect.

Moreover, the rotational inertia, or moment of inertia, of the object is a crucial factor in this process. Moment of inertia quantifies an object’s resistance to changes in its rotational motion and is determined by both the object’s mass and the distribution of that mass around the axis of rotation. An object with a high moment of inertia will experience less rotation in response to a given torque compared to an object with a low moment of inertia.

In summary, the rotation of objects is induced by the application of torque, which is affected by several variables: the magnitude of the force applied, the distance from the axis of rotation, the angle of application, and the object’s moment of inertia.