Answer :
Final answer:
The angular deceleration of the automobile engine is -115.3 rad/s². To calculate the total number of revolutions, the formula for displacement in uniformly accelerated linear motion is used, the result of which is converted to revolutions.
Explanation:
To calculate the angular acceleration, you first need to convert the given speeds from revolutions per minute (rpm) to radians per second (rad/s). The conversion factor is (2π rad)/(1 rev). This gives you 3700 rpm = 3700 * (2π rad) / (60 s) = 387.6 rad/s and 1500 rpm = 1500 * (2π rad) / (60 s) = 157.1 rad/s.
Next, you use the formula for angular acceleration, which is α = Δω / Δt, where Δω is the change in angular velocity and Δt is the elapsed time. So, Δω = ω_final - ω_initial = 157.1 rad/s - 387.6 rad/s = -230.5 rad/s. Thus, the angular acceleration is α = Δω / Δt = -230.5 rad/s / 2.00 s = -115.3 rad/s². The minus sign indicates that it is a deceleration.
To calculate the total number of revolutions, we can make use of the formula for displacement in uniformly accelerated linear motion, Δθ = ω_initial*t + 0.5*α*t², where Δθ is in radians. Converting to revolutions, and substituting the known values, we get the total number of revolutions.
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