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The final angular speeds are:(a)(b)(c)(d)To determine the final angular speed, you can use the following kinematic equation for rotational motion:where:-is the final angular velocity,-is the initial angular velocity,-is the angular acceleration,-is the time.Given values:- Initial angular velocity:- For option (a) and (b),- For option (c) and (d),- Angular acceleration:- For option (a) and (c),rad/s²- For option (b) and (d),rad/s²- TimeNow, substitute the values into the equation to find the final angular speed:(a) For option (a):(b) For option (b):(c) For option (c):(d) For option (d):Now, calculate these values to find the final angular speed for each option.Calculate the final angular speedfor each option:(a) For option (a):(b) For option (b):(c) For option (c):(d) For option (d):So, the final angular speeds are:(a)(b)(c)(d)...