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Answer :
The angular acceleration of the automobile engine slowing down from 3700 rpm to 1100 rpm in 2.6 seconds is approximately -110 rad/s².
The student asked: An automobile engine slows down from 3700 rpm to 1100 rpm in 2.6 s. Calculate its angular acceleration, assumed constant. Express your answer using two significant figures.
To solve this, we can use the formula for angular acceleration:
Angular acceleration (α) = (ωf - ωi) / t
First, we need to convert the angular velocities from rpm (revolutions per minute) to rad/s (radians per second):
- Initial angular velocity (ωi) = 3700 rpm × (2π rad / 60 s) = 388.9 rad/s
- Final angular velocity (ωf) = 1100 rpm × (2π rad / 60 s) = 115.2 rad/s
Next, plug these values into the angular acceleration formula:
α = (115.2 rad/s - 388.9 rad/s) / 2.6 s
α = -105.7 rad/s²
Rounding to two significant figures, the angular acceleration is:
α ≈ -110 rad/s²
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