Final answer:
To calculate the angular speed of the fan in rad/s, convert the angle from degrees to radians and then divide by the time interval. The fan's angular speed is π/3 rad/s or approximately 1.0472 rad/s.
Step-by-step explanation:
The question is asking to calculate the angular speed of a ceiling fan in radians per second (rad/s) when given that the fan rotates at an angle of 45 degrees every 0.75 seconds. To find the angular speed, we first need to convert the angle from degrees to radians because the standard unit for angular speed in physics is rad/s. Using the conversion that 180 degrees is equal to π radians, we can calculate the angular speed as follows:
Angular speed (ω) = angle (ΔΘ) / time (Δt).
First, convert 45 degrees to radians: (45 degrees × π rad) / 180 degrees = 0.25π rad.
Now, divide by the time interval: (0.25π rad) / 0.75 s = π/3 rad/s.
Therefore, the angular speed of the fan is π/3 rad/s, which is approximately 1.0472 rad/s.