Two racing cars of masses m1 and m2 are moving in circles of radii r1 and r2 respectively.
Their speeds are such that each makes a complete circle in the same length of time t.Find the ratio of angular speed of the first car to that of the second car is.

Asked by arpita | 28th Sep, 2014, 09:15: AM

Expert Answer:

Angular velocity is the rate of change of angular displacement with time. 
Given that both the cars complete one circle in the same time 't'
 
begin mathsize 14px style Angular space speed comma straight omega space equals fraction numerator angle space subtended space by space the space car space for space one space revolution left parenthesis 2 straight pi right parenthesis over denominator Time space taken left parenthesis straight t right parenthesis end fraction space space end style
Angular speed of first car,ω1 = 2π / t
Angular speed of the second car, ω2 =2π /t
Therefore the ratio of angular speed of first car to that of second,begin mathsize 14px style fraction numerator straight omega subscript 1 space over denominator straight omega subscript 2 end fraction equals fraction numerator begin display style fraction numerator 2 straight pi over denominator straight t end fraction end style over denominator fraction numerator 2 straight pi over denominator straight t end fraction end fraction equals 1 over 1 end style
The ratio of angular speed of first car to that of second =1:1
  

Answered by Jyothi Nair | 28th Sep, 2014, 10:22: AM