A celing fan with 16 inch blades rotates at 45 revolutions per minute. Find angular speed of fan in radians per minute. Find linear speed of the tips of blades in inches per minute.
45 * 2 pi radians/min = omega
v = omega r
v = 45*2 pi * 16
1440 in/min
To find the angular speed of the fan in radians per minute, we need to convert the given angular speed from revolutions per minute to radians per minute.
Let's start by finding the conversion factor from revolutions to radians. One revolution is equal to 2π radians.
So, the angular speed in radians per minute is:
Angular speed (in radians per minute) = 45 revolutions/minute * 2π radians/revolution
Angular speed (in radians per minute) = 45 * 2π radians/minute
Angular speed (in radians per minute) = 90π radians/minute (approx. 282.74 radians/minute)
Now, let's find the linear speed of the tips of the blades in inches per minute. The linear speed of an object moving along a circular path is equal to the product of the radius and the angular speed.
The radius of the fan blades is 16 inches. Therefore, the linear speed is:
Linear speed (in inches per minute) = 16 inches * 90π radians/minute
Linear speed (in inches per minute) = 1440π inches/minute (approx. 4523.89 inches/minute)
So, the angular speed of the fan is approximately 282.74 radians per minute, and the linear speed of the tips of the blades is approximately 4523.89 inches per minute.
To find the angular speed of the fan in radians per minute, we first need to convert the number of revolutions per minute to radians.
1 revolution is equal to 2π radians.
Therefore, the angular speed in radians per minute can be calculated as follows:
Angular speed (in radians per minute) = Number of revolutions per minute * 2π
In this case, the number of revolutions per minute is 45. So,
Angular speed = 45 * 2π
To find the linear speed of the tips of the blades in inches per minute, we need to calculate the distance traveled by the tip of each blade in one revolution, and then multiply it by the number of revolutions per minute.
To calculate the distance traveled by the tip of each blade in one revolution, we need to find the circumference of the circle formed by the blades. The circumference is equal to the length of each blade path, which is equal to the length of a full circle.
Circumference of a circle = 2π * radius
In this case, the radius is equal to half the length of the blade, which is 16/2 = 8 inches. So,
Circumference = 2π * 8
To find the linear speed of the tips of the blades in inches per minute, we multiply the circumference by the number of revolutions per minute:
Linear speed (in inches per minute) = Circumference * Number of revolutions per minute
Linear speed = 2π * 8 * 45
Now, we can calculate the values:
Angular speed:
Angular speed = 45 * 2π = 90π radians per minute
Linear speed:
Linear speed = 2π * 8 * 45 = 720π inches per minute