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Answer :
Final answer:
The constant angular acceleration can be calculated by first converting revolutions to radians, then using the rotational kinematic equations to find the initial angular velocity, and finally using that to determine the angular acceleration.
Explanation:
To calculate the constant angular acceleration of a wheel given the time it takes to rotate through several revolutions and its angular speed at the end of that interval, you can use the kinematic equation for rotational motion: ωf = ωi + αt, where ωf is the final angular velocity, ωi is the initial angular velocity (which we are trying to find), α is the angular acceleration, and t is the time.
First, we need to find the initial angular velocity. Considering 37.0 revolutions in 2.98 seconds, we convert revolutions to radians by using the conversion factor 2Π radians per revolution.
37.0 rev * 2Π rad/rev = 232.664 radians (approximately).
To find the initial angular velocity (ωi), we use the formula for the angular displacement (θ) which is also part of rotational kinematics: θ = ωi*t + 0.5*α*t^2. Plugging the known values in the equation, we can solve for ωi.
Once ωi is found, we can find the angular acceleration using the original kinematic equation. If we are given the final angular velocity ωf to be 97.3 rad/s, the time t is 2.98 s, and we can plug in ωi to calculate α.
Based on the calculations derived from the given information, the angular acceleration would match one of the options provided in the multiple-choice question, completing the problem.
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