A spherical body moves with a uniform angular velocity x around a circular path of radius r. Which one of the following statements is correct?

For uniform circular motion with constant angular velocity ω, the linear speed is v = ωr and the acceleration is purely centripetal (radial) with magnitude ac = v^2/r = rω^2, directed toward the center of the circular path [1]. Because the angular speed is constant there is no change in the magnitude of velocity, so tangential (linear) acceleration is zero; only the direction changes, producing the inward centripetal acceleration. Standard derivations of circular motion give ac = rω^2 explicitly, independent of the body’s shape or moment of inertia, so factors like 2/5 (a moment-of-inertia factor for spheres) do not enter the linear-acceleration expression [2].

Sources

1. [1] https://www2.tntech.edu/leap/murdock/books/v2chap1.pdf
2. [2] https://openstax.org/books/physics/pages/6-2-uniform-circular-motion