Question

during a 5.1 s time interval, a flywheel with a constant angular acceleration turns through 355 radians and acquires an angular velocity of 116 rad/s. (assume the flywheel is rotating in the positive direction. indicate the direction with the signs of your answers.)

Answer 1

The angular acceleration of the flywheel is 70.59 rad/s^2 in the positive direction.

Step-by-step explanation:

The given information is:

1. Time interval (t)= 5.1 s
2. Angular displacement (θ) = 355 radians
3. Initial angular velocity (ωi) = 0 rad/s
4. Final angular velocity (ωf) = 116 rad/s

We can use the formula:

θ = ωit + (1/2)αt2

Where θ is the angular displacement, ωi is the initial angular velocity, t is the time interval, and α is the angular acceleration.

From the given information, we can rearrange the formula to solve for α:

α = 2(θ - ωit) / t2

Substituting the given values:

α = 2((355 rad) - (0 rad/s)(5.1 s)) / (5.1 s)2

which gives us:

α = 70.59 rad/s2

So, the angular acceleration of the flywheel is 70.59 rad/s2.

Since the angular velocity is increasing, the direction of the angular acceleration is in the positive direction.