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 +190 rad/s. The driver steps on the accelerator, and in a time of 11.0 s the angular velocity increases to +290 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 +190 rad/s during the entire 11.0-s interval? (b) What would have been the angular displacement if the angular velocity had been equal to its final value of +290 rad/s during the entire 11.0-s interval? (c) Determine the actual value of the angular displacement during the 11.0-s interval.

Explanation / Answer

a) angular displacement = w*t=190*11=2090 Radians

b) angular displacement = w*t=290*11=3190 Radians

c) anguar acceleration=[w(final)-w(initial)]/time=(290-190)/11=9.091 rad/s^2

==> angular displacement =[w(final)^2-w(initial)^2]/2*alpha=[290^2-190^2]/(2*9.091)

==> angular displacement =2639.97 Radians

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