A helicopter blade spins at 110 revolutions per minute. Its tip is 5.50 m from the center of rotation.
To solve this problem, we can use the formula for linear velocity, which is given by:
v = 2πr/T
Where:
v = linear velocity (m/s)
r = radius (m)
T = period of rotation (s)
In this case, we need to find the linear velocity of the helicopter blade's tip.
First, we need to convert the rotational speed from revolutions per minute (rpm) to the period of rotation in seconds. To do this, we will use the following conversion factor: 1 minute = 60 seconds.
So, the period of rotation (T) can be calculated as follows:
T = 1/Number of revolutions per second
To convert revolutions per minute to revolutions per second, we divide the given value by 60.
Number of revolutions per second = 110 revolutions per minute / 60
Now, we can calculate the period of rotation (T):
T = 1 / (110/60) = 0.54 seconds
Next, we can substitute the given values for the radius and period of rotation into the linear velocity formula:
v = 2πr/T
v = 2 * 3.14 * 5.50 m / 0.54 s
Simplifying the expression:
v = 34.02 m/s
Therefore, the linear velocity of the helicopter blade's tip is 34.02 m/s.