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Answer :
The angular acceleration of the engine is approximately -257.44 radians per second squared. The engine makes approximately 107 revolutions in 2.6 seconds.
To calculate the angular acceleration of the automobile engine, we can use the formula:
angular acceleration (α) = (final angular velocity - initial angular velocity) / time
Given that the initial angular velocity is 3700 rpm and the final angular velocity is 1200 rpm, and the time taken is 2.6 seconds, we can substitute these values into the formula:
α = (1200 rpm - 3700 rpm) / 2.6 s
Calculating this, we get:
α = (-2500 rpm) / 2.6 s
To convert rpm to radians per second, we multiply by 2π/60:
α = (-2500 rpm) * (2π/60) / 2.6 s
Simplifying this, we find:
α = -257.44 radians per second squared
The negative sign indicates that the engine is slowing down.
Moving on to the second part of the question, we can calculate the number of revolutions the engine makes in 2.6 seconds. We know that the engine starts at 3700 rpm and ends at 1200 rpm, and we can find the average angular velocity by taking the average of the initial and final angular velocities:
Average angular velocity = (initial angular velocity + final angular velocity) / 2
= (3700 rpm + 1200 rpm) / 2
= 2450 rpm
Now, we can calculate the total number of revolutions using the formula:
Number of revolutions = (average angular velocity * time) / (60 rpm)
= (2450 rpm * 2.6 s) / (60 rpm)
Simplifying this, we get:
Number of revolutions = 106.83 revolutions
Rounded to the nearest integer, the engine makes 107 revolutions in 2.6 seconds.
In summary:
- The angular acceleration of the engine is approximately -257.44 radians per second squared.
- The engine makes approximately 107 revolutions in 2.6 seconds.
Note: It's important to understand the formulas used and the units of measurement involved to solve similar problems accurately.
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