wheels keep spinning round

mawalker

1. The problem statement, all variables and given/known data
A car tire is 65.0 cm in diameter. The car is traveling at a speed of 20.0 m/s .

What is the tire's rotation frequency, in rpm?

What is the speed of a point at the top edge of the tire?


What is the speed of a point at the bottom edge of the tire?

2. Relevant equations

i've looked through my book and i'm not even sure what equations to use here.

3. The attempt at a solution


i tried taking 65(20^2) to get rpm and came up with 26000

KoGs

What does rpm stand for? (I know what it stands for, I want to make sure you know)

mawalker

revolutions per minute? correct?

KoGs

Correct. Now they want to know what the tires rotation frequency is. How does frequency relate to time? Is time in seconds or minutes or hours?

mawalker

time is in minutes... seconds * 60

KoGs

Are you sure its seconds * 60 ?

So if it takes me 10 seconds to eat a cheeseburger, you are telling me it takes 10s*60 = 600 minutes to eat that cheeseburger?

mawalker

i mean... seconds /60!

mawalker

so 20/60* .65?

KoGs

I think you are confused with the notation here.
1 min = 60 seconds. You were right the first time. But you do not take the amount of seconds you have and multiply by 60 to get how many minutes we have.

Ok now let's imagine we take our tire and stretch it out into a straight line. How long would this straight line be? Is it it cm's or m's?

Also, rpm does mean revolutions per minute. But explain to me in words what that means. If we take a red marker and dotted the bottom of the tire, after 1 revolution, where is this red dot now?

mawalker

the diameter of the tire is 65 cm. so if it was stretched out then it would be longer than 65 cm.

mawalker

the red dot is at the bottom again. it is the amout of time that it takes for a full rotation, and how many of these rotations are present within the span of one minute.

KoGs

After you stretch it out, it would be longer than 65cm's. But how much longer? You should be able to tell me that with just knowing the diameter. Remember the tire is in the shape of a circle. So really, we want to know the perimeter of the circle. There is a special name for perimeters of circles, and there is also a special formula for it.

And your are correct, that is what rpm is.

mawalker

2pi(r)... = 2(3.14)(65) = 408 cm

mawalker

wait, i mean... r would be half of 65 so 408/2 = 204 cm

KoGs

Almost. r in that formula stands for "radius". A radius of a circle is define to be 1/2 the diameter. That is, 2r = d.

Yup. Ok now what do we want? We want to know how long it takes to go from the start of this length to the end of this length. That would mean it's completed one full revolution right? So how long does it take?

mawalker

so 204 cm.... and it goes 20 m/s, so every second it would go 20 m. or 2000 cm. so 2000/204*60 = 588 rpm?

KoGs

Keep your units!! 2000 what? 204 what? 60 what?

Once you put in the units and multiply through, you should be able to easily see if your answer is in the required rpm units.