Question

An automobile engine slows down from 3900 rpmto 1500 rpm in 2.00 s .

Calculate its angular acceleration, assumed constant.

Calculate the total number of revolutions the engine makes in this time.

Answer 1

Here ,

initial angular speed , wi = 3900 rom

wi = 3900 * 2pi/60 = 408.33 rad/s

wf = 1500 rpm = 1500 * 2pi/60 = 157.1 rad/s

Now , for the angular acceleration

angular acceleration = change in angular speed/time taken

angular acceleration = (157.1 - 408.33)/2

angular acceleration = -125.6 rad/s^2

the angular acceleration is -125.6 rad/s^2

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for the angle

angle = 408.33 * 2 - 0.50 * 125.6 * w^2

angle = 1068 radian = 170 rev

the number of revolutions is 170 Revs