Angular Velocity and Angular Acceleration

In summary, the conversation discusses a problem with finding the angular acceleration and angular velocity for pilots being tested in a human centrifuge. The problem involves using the equations \theta (t) = \theta_0 +\omega_0t + \frac{1}{2}\alpha t^2 and \omega (t) = \omega_0 + \alpha t. The individual has tried finding the frequency and multiplying it by 2\pi, but has not gotten the correct answer. The book provides values for angular acceleration and angular velocity, and the individual is unsure of how to use the units in the equations to find the correct values. They ask for help and eventually figure out the solution.
  • #1
Hotsuma
41
0
I feel really dumb, as this should be incredibly easy to figure out, but I keep getting the wrong answers. I am including the book's data so I can figure out how this needs to be done and then plug in my own values.

Homework Statement



Pilots can be tested for the stresses of flying high-speed jets in a whirling "human centrifuge," which takes 1.0 min to turn through 20 complete revolutions before reaching its final speed.

What is its angular acceleration (assumed constant) (in rev/min^2) and its angular velocity in rpm?

Homework Equations



Code:
\theta (t) = \theta_0 +\omega_0t + \frac{1}{2}\alpha t^2  
\omega (t) = \omega_0 + \alpha t.
[\CODE]

[h2]The Attempt at a Solution[/h2]

I have tried finding the frequency and then multiplying it by 2\pi, but I don't get the right answer. The book's values are: 
Ang. Acc = 40 rev/min^2
Ang. Vel = 40 rpm
 
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  • #2
i think it might have something to do with your units

theta = (1/2).alpha.t^2

you want to find alpha in rev/min^2
so input theta in revolutions and t in mins to get the correct alpha
 
  • #3
I don't think I have a value for theta unless it is 2pi. Even then, that is in radians not revolutions per minute.
 
  • #4
Thanks LowlyPion, my answer for angular acceleration is correct and the concept is much more clear now. I'll let you know if I get angular velocity figured out, which should be easy from here.
 
  • #5
To find Angular velocity I multiply angular acceleration by time. Thanks for the help.
 
  • #6
I forget how to mark this as solved, also, does anyone know how to use direct LaTeX typesetting here?
 

1. What is angular velocity?

Angular velocity is a measure of the rate at which an object rotates or revolves around a fixed point. It is represented by the symbol ω (omega) and is measured in radians per second (rad/s).

2. How is angular velocity different from linear velocity?

Angular velocity is a measure of rotation, while linear velocity is a measure of straight-line motion. Angular velocity is measured in radians per second, while linear velocity is measured in meters per second.

3. What is the relationship between angular velocity and tangential velocity?

Tangential velocity is the linear speed of an object moving along a circular path, and it is directly proportional to the angular velocity. This means that as the angular velocity increases, so does the tangential velocity.

4. How is angular acceleration calculated?

Angular acceleration is the rate of change of angular velocity and is calculated by dividing the change in angular velocity by the change in time. It is represented by the symbol α (alpha) and is measured in radians per second squared (rad/s²).

5. What factors affect angular velocity and angular acceleration?

Angular velocity and angular acceleration are affected by the radius of rotation, the mass and distribution of the object, and the applied torque or force. In addition, angular velocity is also affected by the moment of inertia, which is a measure of how difficult it is to rotate an object.

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