Can someone provide me some input on the question below. Please respond.
A string trimmer is a tool for cutting grass and weeds; it utilizes a length of nylon "string" that rotates about an axis perpendicular to one end of the string. The string rotates at an angular speed of 39 rev/s, and its tip has a tangential speed of 64 m/s. What is the length of the rotating string?
tangential speed= anglarspeed*radius
solve for radius.
To find the length of the rotating string, we need to determine the radius of rotation first.
The formula given is:
Tangential speed = Angular speed * Radius
We are given that the angular speed is 39 rev/s (revolutions per second), and the tangential speed is 64 m/s.
To solve for the radius, we rearrange the formula as follows:
Radius = Tangential speed / Angular speed
Plugging in the given values:
Radius = 64 m/s / 39 rev/s
Now, the units need to be consistent. We can convert rev/s to 1/s by dividing by the number of revolutions in 1 revolution (1 rev = 2π radians). Therefore:
Radius = 64 m/s / (39 rev/s * 2π radians/1 rev)
Simplifying the expression:
Radius ≈ 64 m/s / (77.6π radians/s)
This gives us the radius of rotation.
Finally, to find the length of the rotating string, we use the formula for the circumference of a circle:
Circumference = 2π × Radius
Substituting the value of the radius:
Length of rotating string = 2π × (Radius)
Evaluating the expression, we get the final result for the length of the rotating string.