Angular velocity

**iamanoobatmath** · July 4th 2009, 12:35 PM

A car tire has diameter 64 cm. Determine its angular velocity, in radians per second, when the car is traveling at 100 km/h.

So I want to find the number of rotations the tire makes in one second, and to do that I divide the velocity of the car by the circumference of the tire. (I think)
$100 km/h = 27.78 m/s$

$\pi 64=201.06 cm = .201 m$ is the circumference of the circle in meters.

$\frac{27.78}{.201}=138.5$ is the number of rotations per second.

So the circle makes approximately 138.5 rotations per second. I know that an entire circle is $2\pi$ radians so I just multiple 138.5 by $2\pi$ and that works out to be 870.22 radians/s.

The answer is supposed to be 86.83 radians/s and I don't know what I'm doing wrong. Could someone please explain?

Write an expression for the angular velocity, in radians per second, for a car tire with diameter d centimeters when the car is traveling at x kilometers per hour.

I have no idea how to start this one. Help!

**skeeter** · July 4th 2009, 01:11 PM

angular speed, $\omega = \frac{v}{r}$

$v = 100$ km/hr = $\frac{250}{9}$ m/s

$r = 32$ cm $= .32$ m

$\frac{v}{r} \approx 86.8 rad/s$

**aidan** · July 4th 2009, 01:16 PM

Originally Posted by iamanoobatmath

So I want to find the number of rotations the tire makes in one second, and to do that I divide the velocity of the car by the circumference of the tire. (I think)
$100 km/h = 27.78 m/s$

$\pi 64=201.06 cm = .201 m$ is the circumference of the circle in meters.

$\frac{27.78}{.201}=138.5$ is the number of rotations per second.

So the circle makes approximately 138.5 rotations per second. I know that an entire circle is $2\pi$ radians so I just multiple 138.5 by $2\pi$ and that works out to be 870.22 radians/s.

The answer is supposed to be 86.83 radians/s and I don't know what I'm doing wrong. Could someone please explain?

I have no idea how to start this one. Help!

$\pi 64=201.06 cm = .201 m$ is the circumference of the circle in meters.

check your conversion: 201.06 cm = 2.01 m

Looks as if you have it.

**yeongil** · July 5th 2009, 05:41 AM

Originally Posted by iamanoobatmath

A car tire has diameter 64 cm. Determine its angular velocity, in radians per second, when the car is traveling at 100 km/h.

An alternative (but longer) method would be to make a series of multiplications of different unit ratios, from km/h to rad/s, like this:
$\left(\frac{100 km}{1 hr}\right)\left(\frac{1,000 m}{1 km}\right)\left(\frac{100 cm}{1 m}\right)\left(\frac{1 rad}{32 cm}\right)\left(\frac{1 hr}{60 min}\right)\left(\frac{1 min}{60 sec}\right)$ .

That way, when multiplying out, all of the units cancel except for radians on top and seconds on bottom. I get ~86.81 rad/s as my answer.

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