If an object travels in a circular path of radius R with constant angular speed omega. Find its displacement after time t.

Asked by a.behera67 | 22nd Oct, 2015, 07:25: PM

Expert Answer:

The angular speed of the object is ω.
 
Now, in circular motion angular speed is defined as the rate of change of angular displacement θ.
 
Hence, we have begin mathsize 14px style straight omega equals dθ over dt equals fraction numerator 2 straight pi over denominator straight T end fraction end style.
Now, by completing one full circle the displacement of object will be 2π
 
This displacement will take a time equal to time period T.
 
So, the displacement in time t will be 
begin mathsize 14px style straight theta equals 2 straight pi cross times straight t over straight T straight theta equals fraction numerator 2 straight pi over denominator straight T end fraction straight t therefore straight theta equals ωt end style
 
Hence, the displacement of object after time t is ωt.

Answered by Romal Bhansali | 24th Oct, 2015, 02:17: PM