A car is traveling along a road, and its engine is turning overwith an angular v

Question

A car is traveling along a road, and its engine is turning overwith an angular velocity of +200 rad/s. The driver steps on theaccelerator, and in a time of 9.0 s the angular velocity increasesto +300 rad/s. (a) What would have been theangular displacement of the engine if its angular velocity hadremained constant at the initial value of +200 rad/s during theentire 9.0-s interval? (b) What would have beenthe angular displacement if the angular velocity had been equal toits final value of +300 rad/s during the entire 9.0-s interval?(c) Determine the actual value of the angulardisplacement during the 9.0-s interval.

Explanation / Answer

initial angular speed w = 200 rad / s final angular speed w ' = 300 rad / s time t= 9 s So, angular accleration = ( w ' - w ) / t                                      = 11.11111 rad / s ^ 2 (a). angular velocity w = 200 rad / s time t = 9 s So, angular displacement = w t                                       = 1800 rad (b). angular speed w ' = 300 rad / s time t= 9 s So, angular displacement = w ' t                                       =2700 rad (c). Angular displacement = [ w ' ^ 2 - w ^ 2 ] /2                                           = 2250 rad (b).

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