Final answer:
The angular speed of the fan is 8π rad/min.
Step-by-step explanation:
To find the angular speed of the fan in rad/min, we need to convert the given rotational speed of 40 rpm to rad/min. Since 1 revolution is equal to 2π radians, we can use this conversion factor.
Angular speed (in rad/min) = Rotational speed (in rpm) * 2π
Angular speed = 40 rpm * 2π = 80π rad/min
Therefore, the correct answer is option d) 8π.
The question asks us to find the angular speed of a ceiling fan in radians per minute. To calculate the angular speed in radians per minute, we first understand that the fan completes 40 revolutions per minute (rpm). A single revolution is equal to 2π radians, so the angular speed ω in radians per minute is equal to the number of revolutions per minute times 2π:
ω = 40 rpm × 2π rad/rev
ω = 80π rad/min
Therefore, the correct answer is (d) 8π, which corresponds to an angular speed of 80π rad/min.