High School

A rotating wheel completes 42.5 revolutions in 4.1 seconds with a constant angular acceleration. Its angular speed at the end of this interval is 97.6 rad/s. What is the angular acceleration of the wheel?

A. 9.73 rad/s²
B. 15.8 rad/s²
C. 42.6 rad/s²
D. 23.8 rad/s²
E. None of the above is within 5% of the correct answer.

Answer :

The angular acceleration of the rotating wheel is 9.73 rad/s^2.

Known Values

Given data:

Number of revolutions (n) = 42.5 revolutions

Time taken (t) = 4.1 s

Final angular speed (ω_f) = 97.6 rad/s

Angular Acceleration Formula

The angular acceleration (α) of a rotating object can be calculated using the formula:

α = (ω_f - ω_i) / t

Where:

ω_f = final angular speed

ω_i = initial angular speed (which is 0 rad/s in this case, as the wheel starts from rest)

t = time interval

Calculating Angular Acceleration

Substitute the known values into the formula:

α = (97.6 rad/s - 0 rad/s) / 4.1 s

α = 97.6 rad/s / 4.1 s

α ≈ 23.8 rad/s^2

Therefore, the angular acceleration of the rotating wheel is approximately 23.8 rad/s^2.

The correct answer is option d: 23.8 rad/s^2.

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