Which quantity will change according to how distant the point is from the center?

• A. Mass
• B. Density
• C. Volume
• D. Linear velocity

Answer: (D)

In a rotating system, the rate of rotation (angular velocity) is the same for all points, but the actual speed along the circular path—the linear velocity—depends on how far a point is from the center. The relationship is v = ω r, where r is the distance from the center and ω is the angular velocity. As r increases, v increases proportionally, so points farther from the center move faster along their circular path. Mass, density, and volume don’t change just because you’re looking at a different point on the object; they’re intrinsic properties of the material or the whole object. Therefore, linear velocity is the quantity that changes with distance from the center.