Relation Between Linear And Angular Quantities

NCERT Class 11, Chapter 7 (System of Particles and Rotational Motion) gives the relation between linear and angular speed for a point at perpendicular distance r from the rotation axis as v = rω. A key idea here is that every point on a rigid rotating body shares the same angular velocity ω, since the whole body turns through the same angle in the same time, yet the linear speed depends on how far the point sits from the axis. Points farther from the axis trace larger circles and therefore move faster. Substituting the rim data gives v = 0.50 × 8 = 4 m/s. The option 16 m/s incorrectly divides the angular velocity by the radius instead of multiplying. The option 0.0625 m/s inverts the relation, dividing the radius by the angular velocity. The option 8 m/s simply repeats the angular velocity and ignores the radius factor entirely. A units check confirms that metres multiplied by rad/s gives m/s, because the radian is dimensionless, and 4 m/s is a realistic rim speed for a half-metre wheel turning at 8 rad/s.