Two racing cars of masses m, and m2 are moving in circles of radii r, and r2 respectively. Their speeds are such that each car makes a complete circle in the same time ‘t The ratio of angular speed of the first to that of the second car is :

The angular speed (Δθ/Δt) of an object in circular motion is defined as the rate of change of its angular displacement. For a complete circle, the angular displacement is 2π radians. The time taken to complete one revolution is known as the period (T). The relationship between angular speed (ω) and the period is given by the formula ω = 2π/T. In this scenario, both racing cars complete a circle in the same time 't', meaning their periods are equal (T1 = T2 = t). Since the angular speed depends solely on the time period and is independent of the mass of the cars (m1, m2) and the radii of the circles (r1, r2), the ratio of their angular speeds ω1:ω2 is (2π/t): (2π/t), which simplifies to 1:1.