Step-by-step explanation:
Given: diameter = 16 in
hence radius, r is 16 ÷ 2 = 8 in
a) notice that the fan blades divide the circle into 3 equal sectors.
Each sector is hence 1/3 of the entire circumference of the circle
Arc Length of each sector (between blades),
= (1/3) x circumference
= (1/3) x 2πr
= (1/3) x 2 x 3.142 x 8
= 16.76 in (Answer)
b) similarly, the area between the blades
= (1/3) x πr²
= (1/3) x 3.142 x 8²
= 67.03 in² (answer)
c) The angular velocity is the radians per second that the tip moves
It is given that it moves 8π radians in 2 seconds
hence in 1 second, we expect the tip to move,
8π ÷ 2 = 4π rad/s (Answer)
