Step-by-step explanation:
We can use the formula for tangential acceleration:
a_t = r * α
where a_t is the tangential acceleration, r is the radius of the flywheel, and α is the angular acceleration.
To find the angular acceleration, we can use the formula:
θ = 1/2 * α * t^2
where θ is the angular displacement, t is the time, and α is the angular acceleration.
Rearranging this formula to solve for α, we get:
α = 2θ / t^2
Substituting in the given values, we get:
α = 2 * (2π) / (2.00 s)^2
Simplifying, we get:
α = 1.57 rad/s^2
Substituting this into the formula for tangential acceleration, along with the given radius of the flywheel, we get:
a_t = (0.274 m) * (1.57 rad/s^2)
Simplifying, we get:
a_t = 0.431 m/s^2
Therefore, the magnitude of the tangential acceleration of a point on the rim of the flywheel after 2.00 s of acceleration is approximately 0.431 m/s^2.