Rotating wheel initial angular velocity given final and time

In summary, the rotation wheel had an initial angular speed of 56.98 rad/s based on the given information of completing 37 revolutions in 3.0 seconds with a final angular speed of 98 rad/s. This can be calculated by finding the average angular velocity and subtracting the difference between the final and average velocities. An alternative method using the equations for angular velocity and acceleration can also be used.
  • #1
vinnyzwrx
15
0

Homework Statement


A rotation wheel required 3.0 s to complete 37 revolutions. its angular speed at the end of the 3.0 s interval is 98 rad/s. what was the original angular speed of the wheel?


Homework Equations


average omega = change in angle/change in time


The Attempt at a Solution



heres my thought on the answer, i wanted to make sure its right since i don't have the correct answer to compare my thoughts

i find the average angular velocity by 37*2pi over 3
since the acceleration is constant the average angular velocity is at 1.5 s
so then i find the difference between final angular velocity which is at 3 seconds and the velocity at 1.5 seconds which is 20.51 and subtract that from the average angular velocity to get the angular velocity at 0 seconds.

the final answer is 56.89 since the velocity at 1.5 seconds is 77.49

is this thought process correct, it seems to be from my point of view.
 
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  • #2
That works (though you should check your final answer, it looks like you have a couple digits flipped around.

You can also do this with

[tex]\omega_f^2 = \omega_i^2 + 2 \alpha \Delta \theta[/tex]
and
[tex]\alpha = \frac{\omega_f - \omega_i}{\Delta t}[/tex]

I think your way is probably simpler, but requires breaking the problem into two steps. However, you do avoid having to solve a quadratic equation.
 
  • #3
right, 56.98 rad/s

Thanks!
 

FAQ: Rotating wheel initial angular velocity given final and time

1. What is the equation for calculating initial angular velocity given final angular velocity and time?

The equation for calculating initial angular velocity (ω0) given final angular velocity (ωf) and time (t) is: ω0 = ωf/t.

2. How do I convert the units for angular velocity?

To convert units for angular velocity, you can use the formula ω1 = ω2 * (r1/r2), where ω1 and ω2 are the initial and final angular velocities, and r1 and r2 are the initial and final radii.

3. Can I use this equation for any type of rotating wheel?

Yes, this equation can be used for any type of rotating wheel as long as the initial and final angular velocities are known and the time interval is consistent.

4. What if I have the initial and final angular displacements instead of velocities?

If you have the initial and final angular displacements (θ0 and θf), you can use the formula ω0 = (θf - θ0)/t to calculate the initial angular velocity.

5. How can I apply this equation in real-life scenarios?

This equation can be applied in various real-life scenarios, such as calculating the initial angular velocity of a spinning top or a bicycle wheel, or determining the speed of a rotating fan or a wind turbine. It is also commonly used in engineering and physics experiments involving rotating objects.

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