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Answer :
In this case, the angular acceleration can be found by dividing the final angular velocity by the time. The angular acceleration of the gyroscope is 112.1875 [tex]rad/s^2[/tex].
Angular acceleration (α) is defined as the rate of change of angular velocity (ω). Mathematically, it can be expressed as:
[tex]\alpha = (\omega_f - \omega_i) / t[/tex]
where [tex]\omega_f[/tex] is the final angular velocity, [tex]\omega_i[/tex] is the initial angular velocity (which is zero since the gyroscope starts from rest), and t is the time taken for the acceleration.
In this scenario, the gyroscope is accelerated from rest to an angular velocity of 35.8 rad/s in a time of 0.320 s. Therefore, the final angular velocity ([tex]\omega_f[/tex]) is 35.8 rad/s and the time (t) is 0.320 s.
Using the formula for angular acceleration, we can substitute these values into the equation:
Simplifying the expression, we get:
[tex]\alpha = (35.8 rad/s - 0 rad/s) / 0.320 s[/tex]
[tex]\alpha = 112.1875 rad/s^2[/tex]
Therefore, the angular acceleration of the gyroscope is [tex]rad/s^2[/tex].
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