1. ## Radian Measure

A wheel rotating an an angular velocity of 1.2π radians/s, while a point of circumference of the wheel travels 9.6π m in 10s. What is the radius of the wheel?
I'm not really sure where to start; I know that the wheel makes 36 revolutions in one minute but I'm not sure how to find the circumference or radius. Any suggestions/hints?

I know that the answer is 0.8 m, just not sure how to calculate this.

Please and thank you!

2. ## Re: Radian Measure

$v = r\omega$

$\frac{\9.6\pi}{10} \, m/s = r (1.2\pi \, rad/s)$

3. ## Re: Radian Measure

Originally Posted by misiaizeska
A wheel rotating an an angular velocity of 1.2π radians/s, while a point of circumference of the wheel travels 9.6π m in 10s. What is the radius of the wheel?

The length of the arc subtended by an angle $\theta$ is $L=r\theta$.

4. ## Re: Radian Measure

I presume you know that circumference of a circle of radius r is $2\pi r$. That divides into $9.6\pi$ 4.8/r times so the wheel must have turned through 4.8/r revolutions. Since each revolution is $2\pi$ radians, that will be $(4.8/r)(2\pi)= (9.6/r)\pi$ radians. Since we are told that the wheel turned at $1.2\pi$ radians per second for 10 seconds, it actually turned through 12 radians: 9.6/r= 12. Solve that for r.

5. ## Re: Radian Measure

I used this formula - thanks to everyone!