A car engine is initially rotating at 180 rad/s. It is then turned off and takes 1.20 s to come to a complete stop. What is the angular acceleration of the engine? Assume acceleration is constant.
ω=ωₒ + ε•t,
ω =0,
ε = - ωₒ/t = - 180/1.2 = - 150 rad/s²
To find the angular acceleration of the car engine, we can use the formula:
Angular acceleration (α) = (Final angular velocity (ωf) - Initial angular velocity (ωi)) / Time (t)
Given:
Initial angular velocity (ωi) = 180 rad/s
Final angular velocity (ωf) = 0 rad/s
Time (t) = 1.20 s
We can substitute these values into the formula to find the angular acceleration:
α = (0 - 180) / 1.20
Now, we can calculate:
α = (-180) / 1.20
Simplifying further, we get:
α = -150 rad/s^2
Therefore, the angular acceleration of the car engine is -150 rad/s^2.
Note: The negative sign indicates that the angular acceleration is in the opposite direction of the initial angular velocity, which means the engine is slowing down.