Velocity In Rolling Motion

In rolling without slipping, the contact point with the ground is instantaneously at rest, and every other point's velocity is the vector sum of the centre's translation $v$ and the rotation $\omega r$ about the centre. The no-slip condition fixes $\omega =v/R$, so the rim speed relative to the centre equals $v$ itself. At the topmost point the translational velocity $v$ and the rotational velocity $\omega R=v$ point in the same forward direction and therefore add: $v_{top}=v+v=2v=2\times 5=10\text{ m/s}$. The value 5 m/s gives only the centre's speed and ignores the rotational contribution. The value 0 m/s describes the bottom contact point, not the top. The value 7.5 m/s uses an incorrect intermediate factor of 1.5. This is the NCERT velocity analysis of a rolling wheel. As a check, the top must be the fastest point of the wheel, exceeding the centre's 5 m/s, and 10 m/s correctly captures that maximum. More generally, every point on the rim traces a cycloidal path as the wheel advances, with its speed ranging from zero at the ground contact to twice the hub speed at the very top, while a point level with the axle moves at $\sqrt{2}v$.