A car is traveling along a road, and its engine is turning over with an angular

Question

A car is traveling along a road, and its engine is turning over with an angular velocity of +230 rad/s. The driver steps on the accelerator, and in a time of 9.0 s the angular velocity increases to +270 rad/s. (a) What would have been the angular displacement of the engine if its angular velocity had remained constant at the initial value of +230 rad/s during the entire 9.0-s interval? (b) What would have been the angular displacement if the angular velocity had been equal to its final value of +270 rad/s during the entire 9.0-s interval? (c) Determine the actual value of the angular displacement during the 9.0-s interval.

Explanation / Answer

Given i = 230 rad/s, f = 270 rad/s

time , t = 9.0s

a)1 = i * t = 230 rad/s *9.0 s = 2070 rad

b)First we find angular acceleration

   = (f - i)/t = (270 - 230)rad/s / 9s

   = 4.44 rad/s^2

Now = i * t +1/2t^2

          = 2070 + 0.5 *4.44 *(9)^2

   2 2250 rad

c)Actual angular displacement , = 2 - 1

                                    = 2250 rad - 2070 rad = 180rad

  

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