Math Is Fun Forum

Anakin

Member

Registered: 2009-10-04

Posts: 145

Angular Velocity

So here is the question:

"A car is traveling at 100 km/h and the tire of the car has a radius of 36cm. Find the number of revolutions per second."

Process:

100 km/h * (10,000,000 cm/km) * (1h/3600 secs) = 2777.77777778 cm/s is the speed of the car.

Θ = a/r
Θ = (2777.78) / (36)
Θ = 77.16

To find number of revolutions, we must divide by 2pi.

77.16/2pi = 12.28 revolutions/sec. That is the correct answer.

a) I did not get that on the quiz because I do not understand the mechanics behind the operation. Can anyone walk me through each calculation and state why that step is done?
b) And why is 2777.78 cm/s equal to the arc length? Isn't arc length a distance? I thought 2778.78 cm/s was a velocity measurement.

Thank you.

Last edited by Anakin (2009-11-15 11:00:22)

Anakin

Member

Registered: 2009-10-04

Posts: 145

Re: Angular Velocity

Nevermind, I thought of it quite a bit and I think I've got the concept.

But just to make sure:

First 100 km/h is converted into 2777.78 cm/s. That is the speed at which the tire travels. So basically, every second, it moves 2777.78 cm. This would make it the arc length.

Now we have to look at it in a perspective of ONE SECOND intervals.

So Θ = a/r
Θ = 77.16 is the value of the angle in radians but for ONLY ONE SECOND.

Then we must find out how many times it rotates in one second or how many revolutions it has so we divide that number by 2pi.

Is my understanding correct?

Last edited by Anakin (2009-11-15 14:53:22)

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Angular Velocity

That looks more or less right.
One thing - to convert from km to cm, you multiply by 100,000. But you then carry on to get the right answer anyway, so it's just a small error.

---

Why did the vector cross the road?
It wanted to be normal.

Anakin

Member

Registered: 2009-10-04

Posts: 145

Re: Angular Velocity

Thanks Mathsyperson.