Find the rotation in revolutions per minute given the angular speed and the radius given the linear speed and the rate of rotation.
1. w= 2.7 rad/s
2. v=24.8 m/s, 120 rev/min
3. w= 4/3Pi rad/hr
Please help me with these problems! I am a visual learner and I learn best when steps are provided. Thanks in advance!
Sure! I'll walk you through each of these problems step by step.
1. To find the rotation in revolutions per minute, given the angular speed (w) in radians per second, we'll use the formula:
Rotation (in revolutions per minute) = (angular speed / (2π)) * 60
So for the given angular speed of w = 2.7 rad/s, we can substitute it into the formula:
Rotation = (2.7 / (2π)) * 60
Now, let's calculate it:
Rotation = (2.7 / (2 * 3.14159)) * 60
Rotation ≈ 25.71 revolutions per minute
Therefore, the rotation is approximately 25.71 revolutions per minute.
2. To find the rotation in revolutions per minute, given the linear speed (v) in meters per second and the rate of rotation, we'll use the formula:
Rotation (in revolutions per minute) = (linear speed * 60) / (2π * rate of rotation)
For the given values v = 24.8 m/s and rate of rotation = 120 rev/min, we can substitute them into the formula:
Rotation = (24.8 * 60) / (2π * 120)
Let's calculate it:
Rotation = (24.8 * 60) / (2 * 3.14159 * 120)
Rotation ≈ 1.31 revolutions per minute
Therefore, the rotation is approximately 1.31 revolutions per minute.
3. To find the rotation in revolutions per minute, given the angular speed (w) in radians per hour, we'll use the formula:
Rotation (in revolutions per minute) = (angular speed / (2π)) * 60 * 60
For the given angular speed w = (4/3)π rad/hr, we can substitute it into the formula:
Rotation = ((4/3)π / (2π)) * 60 * 60
Now, let's calculate it:
Rotation = ((4/3)π / (2 * 3.14159)) * 60 * 60
Rotation ≈ 1200 revolutions per minute
Therefore, the rotation is approximately 1200 revolutions per minute.
I hope this explanation helps! Let me know if you have any further questions.