# Thread: Angular velocity

1. ## Angular velocity

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)
$\displaystyle 100 km/h = 27.78 m/s$

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

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

So the circle makes approximately 138.5 rotations per second. I know that an entire circle is $\displaystyle 2\pi$ radians so I just multiple 138.5 by $\displaystyle 2\pi$ 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!

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

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

$\displaystyle r = 32$ cm $\displaystyle = .32$ m

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

3. 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)
$\displaystyle 100 km/h = 27.78 m/s$

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

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

So the circle makes approximately 138.5 rotations per second. I know that an entire circle is $\displaystyle 2\pi$ radians so I just multiple 138.5 by $\displaystyle 2\pi$ 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!

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

check your conversion: 201.06 cm = 2.01 m

Looks as if you have it.

4. 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:
$\displaystyle \left(\frac{100 km}{1 hr}\right)\left(\frac{1,000 m}{1 km}\right)\left(\frac{100 cm}{1 m}\right)\left(\frac{1 rad}{32 cm}\right)\left(\frac{1 hr}{60 min}\right)\left(\frac{1 min}{60 sec}\right)$.

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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### what is tje angular velovity of a car tire of diameter 64 cm travelling at 100km per hour

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