How Many Revolutions Does a Tire Make Before Wearing Out?

[rockmorg]

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

 

[rockmorg]

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

 

[quicknote]

,

Rotational kinematics involves the study of motion and rotation of objects. In order to solve these problems, we need to use equations that relate the angular velocity, rotational speed, and distance traveled.

For the first question, we can use the equation Vt = rw to find the tangential velocity of the tire. Then, we can use the formula for angular velocity, ω = Δθ/Δt, to find the number of revolutions the tire makes before wearing out. We know that the distance traveled is 98,000 km and the radius of the tire is 0.35 m, so we can plug these values into the equations and solve for Δθ. This will give us the number of revolutions the tire makes before wearing out.

For the second question, we can use the same equations to solve for the number of revolutions the diver makes on the way down. We know the height of the cliff, so we can use the formula for displacement, s = ½at², to find the time the diver spends in the air. Then, we can use the formula for angular velocity to find the number of revolutions during that time.

I hope this helps you with your homework. Remember to always carefully read the problem and identify the known and unknown variables before applying the equations. Good luck!