Final answer:
The magnitude of the angular acceleration of the salad spinner is calculated using kinematic equations for rotational motion, resulting in 2.62 rad/s^2, which does not correspond to the provided options, indicating a possible error in the question or options.
Step-by-step explanation:
To find the magnitude of the angular acceleration of the salad spinner, we can use the kinematic equations for rotational motion given that the spinner slows down with a constant angular acceleration.
Firstly, we know the spinner makes 20.0 rotations in 5.00 seconds, which means the initial angular velocity (ωi) can be calculated as:
ωi = (20.0 revolutions) / (5.00 s) = 4.0 revolutions per second. Converting revolutions to radians:
ωi = (4.0 rev/s) * (2π rad/rev) = 8π rad/s
It then makes 6.00 more rotations before stopping, which equals:
Total angle (θ) = 6.00 revolutions * 2π rad/rev = 12π rad
Applying the kinematic equation for constant angular acceleration:
θ = ωit + (1/2)αt2
Since the spinner stops, the final angular velocity (ωf) is 0. Let's solve for the angular acceleration (α):
12π rad = (8π rad/s)t + (1/2)αt2
We know that the spinner stops with 6 more revolutions, but we do not know the time it takes to do so. We can use another kinematic equation:
ωf2 = ωi2 + 2αθ
0 = (8π rad/s)2 + 2α(12π rad)
0 = 64π2 rad2/s2 + 24π rad α
α = - 64π2 rad2/s2 / 24π rad
α = -8π / 3 rad/s2
α = -2.61799 rad/s2
The magnitude of the angular acceleration is therefore 2.62 rad/s2, which is not an option provided in the multiple choices. There seems to be an issue with the provided options or the question setup.