A car travels along a road & its engine is turning over with angular velocity of

Question

A car travels along a road & its engine is turning over with angular velocity of +220 rad/s. Driver accelerates and in a time of 11.0s, the angular velocity increases to +300 rad/s.
-What would have been the angular displacement of the engine:
(a)if its angular velocity remained constant at its initial value(+220 rad/s) during the entire 11.0s
(b)if its angular velocity had equaled its final value(+300 rad/s) during the entitre 11.0s
And:
(c)what is the actual angular displacement during the 11.0s interval

Explanation / Answer

Assuming the angular velocity is constant at 220 rad/s,

there is noangular acceleration, so:

= o*t + (1/2)*t2
but, = 0
= *t = (220 rad / s) * (11 s) = 2420radians.

Assuming the angular velocity is constant at 300 rad/s,

there is noangular acceleration, so:

= o*t + (1/2)*t2
but, = 0
= *t = (300 rad/s) * (11s) = 3300radians.

Now, assuming the angular velocity does change,

then we must solvefor angular acceleration:
= o + t
(300 rad/s) = (220rad/s) + (11s)
= 80/11 rad / s2

And, to solve for :
= o*t + (1/2)*t2
= (220 rad/s)*11 + (1/2)*(80/11rad/s^2)(11)2
= 2860radians

Notice the true value is simply the average of the

angulardisplacements from part 1 and 2, respectively.

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