AProportional to its distance from the axis
BThe same for all particles
CInversely proportional to its distance from the axis
DAlways zero
Answer:
B. The same for all particles
Read Explanation:
Understanding Angular Velocity in Rigid Bodies
Definition of a Rigid Body
A rigid body is an idealized model of a solid body where deformation is neglected or assumed to be negligible. This means the distance between any two particles within the body remains constant, regardless of external forces applied.
Angular Velocity
Angular velocity (often denoted by the Greek letter $\omega$) is the rate of change of angular displacement of a particle or body. It measures how fast an object rotates or revolves relative to a point or axis, and the direction of the rotation.
It is a vector quantity. Its magnitude is the angular speed, and its direction is along the axis of rotation, following the right-hand rule (if you curl the fingers of your right hand in the direction of rotation, your thumb points in the direction of the angular velocity vector).
Angular Velocity in a Rigid Body about a Fixed Axis
When a rigid body rotates about a fixed axis, every particle in the body completes one full revolution in the same amount of time. This means they all have the same period of rotation and thus the same frequency of rotation.
Consequently, all particles in a rigid body rotating about a fixed axis have the same angular velocity, regardless of their distance from the axis of rotation.
Key Distinction: While the angular velocity is the same for all particles, their linear velocity (v) is not. The linear velocity of a particle is given by $v = \omega r$, where $r$ is the perpendicular distance of the particle from the axis of rotation. This implies that particles farther from the axis move faster linearly than particles closer to it.