Math Help - Angular Speed and Velocity Problem

1. Angular Speed and Velocity Problem

A circle of radius 8 in. is rotating 15o/sec. What is the linear speed v, the angular speed in RPM and the angular speed in rad/sec?

So at first I tried converting the 15o/sec to velocity, by having the degrees become inches. This will then have the measurement in/sec.
But one thing I am confuse is with converting 15o to inches, can anyone help?

2. Re: Angular Speed and Velocity Problem

Originally Posted by Chaim
A circle of radius 8 in. is rotating 15o/sec. What is the linear speed v, the angular speed in RPM and the angular speed in rad/sec?

So at first I tried converting the 15o/sec to velocity, by having the degrees become inches. This will then have the measurement in/sec.
But one thing I am confuse is with converting 15o to inches, can anyone help?
you cannot convert degrees to inches .. they are not the same type of measurement. degrees are an angle measure; inches are a measure of length.

start by converting degrees to radians ... $(degrees) \cdot \frac{\pi}{180} = radians$

once you have angular speed, $\omega$ , in radians/sec, then linear speed , $v = r\omega$

to convert angular speed from radians per second to RPM ...

$\left(\frac{radians}{sec}\right) \cdot \left(\frac{1 \, revolution}{2\pi \, radians}\right) \cdot \left(\frac{60 \, sec}{min}\right) = \frac{revolutions}{min}$

3. Re: Angular Speed and Velocity Problem

Thanks! That makes so much sense now
But I was wondering, when I'm converting degrees into radians, why would that be the angular speed? Just wondering, cause I checked the internet of converting degrees, but do not understand how I would know that would be the angular speed

4. Re: Angular Speed and Velocity Problem

Originally Posted by Chaim
But I was wondering, when I'm converting degrees into radians, why would that be the angular speed? Just wondering, cause I checked the internet of converting degrees, but do not understand how I would know that would be the angular speed