Answer:
a) The length of an arc between two consecutive fan blades is 16.76 inches
b) The area of each sector is 67.02 inches²
c) The angular velocity is 4m rad/sec
Step-by-step explanation:
* Lets explain how to solve the problem
- The fan has three thin blades that spin to produce a breeze
- The diameter of the fan is 16 inches
- The three blades divided the circle into three equal parts
- The circumference of the circle is 2πr
a)
∵ The diameter of the circle = 16 inches
∵ The radius of the circle is half the diameter
∴ The radius (r) = 1/2 × 16 = 8 inches
∵ The length of the circle = 2πr
∴ The length of the circle = 2π(8) = 16π
- The length of an arc between two consecutive fan blades is 1/3
the length of the circle
∴ The length of the arc = 1/3 × 16π = 16.76 inches
* The length of an arc between two consecutive fan blades is
16.76 inches
b)
- The area of a sector in the circle = [tex]\frac{x}{360}(\pi r^{2})[/tex]
where x is the central angle of the sector and r is the radius
of the circle
∵ The angle between each two consecutive blades = 360°/3
∴ x = 360°/3 = 120°
∵ r = 8 inches
∴ The area of each sector = [tex]\frac{120}{360}(\pi )(8^{2})=67.02[/tex]
* The area of each sector is 67.02 inches²
c)
∵ The angular velocity = Ф rad ÷ t, where Ф is the central angle
with radian measure and t is the time in seconds
∴ ω = Ф/t radian/second
∵ Ф = 8m radians
∵ t = 2 seconds
∴ ω = 8m ÷ 2 = 4m rad/sec
* The angular velocity is 4m rad/sec
