How Many Revolutions Does a Tire Make Before Wearing Out?

AI Thread Summary
The discussion revolves around two physics problems related to motion and revolutions. The first question involves calculating the number of revolutions a tire makes before wearing out, given a distance of 98,000 km and a tire radius of 0.35 m. The second question focuses on a diver's rotational motion as she falls from a 7.1 m cliff, needing to determine the number of revolutions based on her average angular speed of 1.0 rev/s. The original poster expresses frustration with the calculations but later finds assistance through research. Overall, the thread highlights common challenges in applying rotational kinematics to real-world scenarios.
rockmorg
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Hey all I have a couple questions about some homework that I've been working on...

1 -
The warranty on a new tire says that an automobile can travel for a distance of 98,000 km before the tire wears out. The radius of the tire is 0.35 m. How many revolutions does the tire make before wearing out?

I've been trying to use Tangential Velocity (Vt) = rw to somehow solve this because I did a similar problem just before it like this, no avail...

2-
At the local swimming hole, a favorite trick is to run horizontally off a cliff that is 7.1 m above the water. One diver runs off the edge of the cliff, tucks into a "ball," and rotates on the way down with an average angular speed of 1.0 rev/s. Ignore air resistance and determine the number of revolutions she makes while on the way down.

Supposedly, I should be able to do this with a rotational kinematics equation... but it just is not working out. I'm guessing I need the time in the air so I can find the number of revolutions during that time...

Grrr... any help would be appreciated, thanks!

-
Morgan
 
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I'm going to reply to my own post and let everyone know I did a nifty search and found help for my problems, yay! Thanks to all those who checked out my post...

-
Morgan
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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