Consider a spherical globe rotating about an axis passing through its poles. There are three points P, Q, and R situated...

Question

Consider a spherical globe rotating about an axis passing through its poles. There are three points P, Q, and R situated respectively on the equator, the north pole, and midway between the equator and the north pole in the northern hemisphere. Let P, Q, and R move with speeds v_P, v_Q, and v_R respectively. Which one of the following options is CORRECT?

A. v_Q < v_R < v_P
B. v_R < v_Q < v_P
C. v_R < v_P < v_Q
D. v_Q < v_P < v_R

Accepted Answer

v_Q < v_R < v_P — Option A is correct. When a sphere rotates about its polar axis, every point completes one full revolution in the same time period T. However, a point's linear speed depends on the radius of the circular path it traces. A point on the equator traces the largest circle (radius R), a point at the pole stays fixed (radius 0), and a point at mid-latitude traces a circle of radius R*sin(45°) = R/sqrt(2). So the closer a point is to the equator, the faster it moves linearly.