Final answer:
All particles on a rotating body have the same angular velocity because it represents the rate of rotation, while their linear velocities differ due to varying distances from the rotation axis, which affects the circumferential distance covered during rotation.
Step-by-step explanation:
In a rotating body, all particles have the same angular velocity because angular velocity is defined as the rate of change of the angular position of the body as a whole with respect to time. Angular velocity is represented mathematically as ω = dθ/dt and is a scalar quantity that tells us how fast the rotation occurs. However, the linear velocity of each particle varies because it is dependent on the distance of each particle from the axis of rotation. While angular velocity gives us the speed of rotation regardless of where the particles are located on the rotating object, linear velocity, which is tangent to the motion, is calculated by the relation v = rω, where r is the radius or the distance of the particle from the axis of rotation. Therefore, particles that are further away from the rotation axis will have a greater circumference to cover in one rotation and must move faster to complete a rotation at the same time, leading to a greater linear velocity.