How to find angular velocity without being given time?

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You do have the initial angular velocity; it is given as 32 rad/s.

The angular acceleration is $-0.7$ rad/$s^2$, it is negative because the gyro is slowing.

So to find the stopping time you have to solve $$ 32 - 0.7 t = 0 \\ t = 320/7 \approx 45.71 $$ Now you need to compute the number of revolutions, and here a trick is to note that the average angular velocity will be exactly half the initial angular velocity, since it is slowing with constant deceleration.

$$ \bar{\omega} = {16.0} \\ N_{\mbox{revolutions}}= \frac{t \bar{\omega} }{2\pi}= \frac{16\times 320}{14\pi} \approx 116.41 $$

So it will make $114$ complete revolutions, and a smidgen more.

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tyger2020
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Updated on September 12, 2020

Comments

  • tyger2020
    tyger2020 about 3 years

    A gyroscope slows from an initial rate of 32.0 rad/s at a rate of 0.700 rad/seconds squared. How many revolutions does it make before stopping?

    If only I could find the angular velocity first, in radians/second...

    I'm assuming 0.700 rad/second squared is angular acceleration, and so far I have only been taught equations to find angular acceleration with time, and I don't know time.

    How do I find angular velocity given this information? Once I get there, I can convert it to revolutions.

    • Ivan Lerner
      Ivan Lerner about 6 years
      You do have the angular velocity, it is the first number given in the question, and it changes linearly by 0.7rad/s per second. When asking questions it is better to show what you have tried so that we can see where you are having trouble with, since often you think you are having trouble with something, but it is actually something else that is confusing you. (downvoted until you improve the question, since I'm not just gonna give you the answer)