15.2:
Rotational Motion about a Fixed Axis
When a rigid body rotates about a fixed axis, any given point within that body moves in a circular path around a specified line or point.
This type of rotation is defined by the angular position, represented by the angle θ which is measured from a fixed reference line to the rotating object.
The change from this angular position, quantified as a differential dθ, is termed angular displacement. The magnitude of this displacement can be measured in degrees, radians, or revolutions. Here, one revolution equal to 2π radians.
The right-hand rule gives the direction of angular displacement, which is along the axis of rotation.
Angular velocity, denoted as ω, describes the rate of change of angular displacement. Angular velocity is measured in units of radians per second.
Furthermore, angular acceleration, denoted as α, is the rate of change of angular velocity. It is measured in the units of radians per second squared.
Similar to angular displacement; both angular velocity and angular acceleration are vector quantities directed along the axis of rotation.
15.2:
Rotational Motion about a Fixed Axis
A rigid body's rotation around a fixed axis makes every point within it trace a circular path around a specific line or point. The term given to this type of spinning is defined by the angular position, symbolized by the angle θ. This angle is gauged from a static reference line to the revolving object. From this angular position, any variation is referred to as angular displacement, denoted by dθ. The extent of this displacement can be calculated in degrees, radians, or revolutions, where one revolution equals 2π radians. This measurement helps in understanding the object's position in its rotational motion. The direction of angular displacement is determined by the right-hand rule, which means it aligns with the rotation axis.
Another aspect of rotational motion is angular velocity, symbolized by ω. It signifies the speed at which angular displacement changes and is quantified in radians per second. Angular velocity defines the rate at which the angular displacement changes over time and is measured in radians per second. Additionally, the concept of angular acceleration comes into play, symbolized by α. Angular acceleration indicates how quickly or slowly the angular velocity changes over time. It is measured in the units of radians per second squared.
Like angular displacement, both angular velocity and angular acceleration are vector quantities, meaning they have both magnitude and direction. These vectors are oriented along the axis of rotation, indicating the direction of the rotation.
Understanding these concepts is fundamental to grasp the mechanics of rotational motion. They provide a comprehensive framework to comprehend how objects rotate and the forces that influence their movement.