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 +220 rad/s. The driver steps on the accelerator, and in a time of 13.0 s the angular velocity increases to +300 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 +220 rad/s during the entire 13.0-s interval? (b) What would have been the angular displacement if the angular velocity had been equal to its final value of +300 rad/s during the entire 13.0-s interval? (c) Determine the actual value of the angular displacement during the 13.0-s interval.

Explanation / Answer

intial angular angular velocity =w1 = 220 rad/s final angular angular velocity =w2 = 300 rad/s intervel of time =t = 13 sec (a) if the angular velocity would have been kept at 220 rad/s during the entire intervel of time t=14s the angular displacement =angular velocity. time =220(13) rad =2860 rad (appx.) (ans) (b) if the angular velocity would have been kept at 300 rad/s during the entire intervel of time t=14s the angular displacement =angular velocity. time =300(13) rad =3900 rad (appx.) (ans) (c) the actual value of angular displacement is given by the standered formula as, w2^2 -w1^2 = 2(angular acceleration)(angular displacement)---------(1) but, angular acceleration = w2-w1/t =300-220/13 rad/s^2 =6.154 rad/s^2 (appx.) from equn. (1) , the angular displacement = w2^2 -w1^2 /2(angular acceleration) =(300)^2 -(220)^2 /2(6.154) rad = 3379.92 rad (appx.) (ans)

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