A ventilation fan has blades 0.25 m in radius rotating at 20rpm. What is the tangential speed of each blade tip?
i don't understand how to do tangential speed.
The tip travels 2*pi*0.25*20 meters (in a circle) in 60 seconds.
That is a tangential speed of 0.524 m/s
Are you sure the rotation rate is only 20 rpm? That is VERY slow for a fan.
20 rev/second is more likely for a ventialation fan.
Ah, tangential speed, the sneaky little cousin of linear speed. Don't worry, I'll break it down for you in a way that won't blow you away!
First, let's find out how far the tip of the blade travels in one revolution (one revolution = 20 rpm). The formula to find the circumference of a circle is C = 2πr (where r is the radius), so in this case, C = 2π(0.25) = 1.57 meters.
Now, to figure out the tangential speed, we need to find out how much distance is covered in one minute, since rpm stands for revolutions per minute. Since the distance covered in one revolution is 1.57 meters, the tangential speed would be 1.57 meters * 20 revolutions = 31.4 meters per minute.
So, the tangential speed of each blade tip is 31.4 meters per minute. Just remember, this is tangential speed, not a tornado speed!
To find the tangential speed of the blades, you need to use the formula:
Tangential Speed = Radius x Angular Speed
In this case, the radius of the blades is given as 0.25 m, and the angular speed is given as 20 rpm (revolutions per minute).
However, the angular speed should be converted to radians per second (rad/s) before using the formula. Since 1 revolution is equal to 2π radians, we can convert 20 rpm to rad/s as follows:
Angular Speed (in rad/s) = (20 rpm) x (2π rad/1 revolution) x (1 min/60 s)
Angular Speed (in rad/s) = 2π × (20/60) rad/s = (2π/3) rad/s
Now, we can substitute the values into the formula:
Tangential Speed = (0.25 m) x (2π/3 rad/s)
Calculate the value of the expression to find the tangential speed.
To calculate the tangential speed, you need to determine the linear speed of an object moving in a circular path. Tangential speed represents the velocity of an object as it moves along the tangent of the circle at any given point.
To find the tangential speed of each blade tip on a ventilation fan, you can follow these steps:
1. Convert the rotational speed from revolutions per minute (rpm) to radians per second (rad/s). Since 1 revolution is equal to 2π radians, use the conversion factor of 2π rad/1 rev.
Tangential speed = Rotational speed × 2π
2. Calculate the circumference of the circle that the blade tip travels along. The circumference of a circle is given by the formula:
Circumference = 2π × radius
In this case, the radius is given to be 0.25 m.
3. Multiply the rotational speed in radians per second by the circumference of the circle to find the tangential speed.
Tangential speed = Rotational speed × Circumference
Let's calculate the tangential speed using the given information.
Given:
Radius of the blades = 0.25 m
Rotational speed = 20 rpm
Step 1: Convert the rotational speed from rpm to rad/s
Rotational speed = 20 rpm × (2π rad/1 rev) = 40π rad/min
To convert from rad/min to rad/s, divide the value by 60:
Rotational speed = (40π rad/min) ÷ 60 = 2π/3 rad/s
Step 2: Calculate the circumference
Circumference = 2π × 0.25 m = 0.5π m
Step 3: Find the tangential speed
Tangential speed = (2π/3 rad/s) × (0.5π m) = π^2/3 m/s
Therefore, the tangential speed of each blade tip on the ventilation fan is approximately π^2/3 m/s.