Question

Calvin is dancing with Hobbes in the middle of the night. Starting with an angular velocity of 4 rad/s, they gradually slow down at a constant rate until they come to a complete stop in 12 seconds. How many revolutions did they make during this time?

Answer 1

Given

   Calvin dancing initially with angular velocity W1 = 4 rad/s,
gradually the speed decreasing and comes to rest in time t = 12 s

the numbero revolutions made in this time is n = ?

   the angular displacement covered in time 12 s is

  
the angular acceleration is W2 = W1 - alpha*t
      

           alpha = W1/t = 4/12 = 0.333 rad/s2

now the angular displacement is theta = w1t+0.5*alpah*t^2
               = 4*12 + 0.5*0.333*12^2 rad
               = 71.976 rad

   the number of revolutions is 71.976/2pi= 111.455 revolutions