A community for students.

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

anonymous

  • 5 years ago

Ball moving at 18 rads/s slows down at a rate of 2 rads/s^2 how many rev's does it do before it stops?

  • This Question is Closed
  1. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    It will do \[\frac{81}{2\pi}\]revolutions. I'll prove it in a second.

  2. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    This is kinematic rotational motion. We develop the equations as such:

  3. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    ...and since you've disappeared, I'm thinking you're not interested.

  4. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    I'm here sry

  5. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    13 rev total but now I'm not so sure

  6. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Okay. Angular acceleration is the second derivative of \[\theta (t)\] that is,\[\frac{d^2 \theta}{dt^2}=\alpha\]If you integrate with respect to time, you get\[\frac{d \theta }{dt }=\alpha t + \omega _0\]where omega_0 is the initial rotational speed. Integrate again to get the angle swept out as a function of time\[\theta =\frac{1}{2}\alpha t^2+\omega_0t+\theta_0\]Theta_0 is the initial angle the system starts at (with respect to the standard x-y axis). Since we're only interested in the change in theta (so we can work out the number of revolutions), we can write\[\Delta \theta = \frac{1}{2}\alpha t^2+\omega_0t\](more's coming).

  7. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Nothing is mentioned about time in the question, so we need to eliminate it from the equation above. We know, from out calculations that,\[\omega = \alpha t + \omega _0\]so that\[t=\frac{\omega - \omega_0}{\alpha}\]Substitute this into the equation for the total angle swept out to get,\[\Delta \theta = \frac{1}{2}\alpha \left( \frac{\omega - \omega_0}{\alpha} \right)^2+\omega_0\left( \frac{\omega-\omega_0}{\alpha} \right)\]You can simplify this, but since you're only after a number, there's not much point. So, to use it, we know that it has\[\omega_0 = 18 ^cs^{-1}\]\[\alpha = -2^cs^{-1}\]and that, since in the end, it's not moving,\[\omega = 0\]Substituting these values into Delta theta gives you\[\Delta \theta = 81^c\]

  8. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Now, this is the total amount of radians swept out, not the revolutions, but we know that there are \[2\pi \frac{rad}{rev}\](i.e. 2pi radians per revolution) and so the number of revolutions is\[n=\frac{81 rad}{2\pi rad/rev}=\frac{81}{2\pi}rev \approx 12.89rev\]

  9. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    You could have also solved for the time in omega = alpha t + omega_0, and then sub'd that value into the Delta theta expression. The time you get is 9 seconds.

  10. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Thx, didn't really know there was people that could help with physics

  11. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    np. I'd appreciate another fan, that took forever to write out ;p

  12. anonymous
    • 5 years ago
    Best Response
    You've already chosen the best response.
    Medals 0

    Really thx a lot though I might be asking so more here soon, that's the best I've seen explained yet

  13. Not the answer you are looking for?
    Search for more explanations.

    • Attachments:

Ask your own question

Sign Up
Find more explanations on OpenStudy
Privacy Policy

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.