Angular Speed and Velocity Problem

[Chaim]

A circle of radius 8 in. is rotating 15^o/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 15^o/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 15^o to inches, can anyone help?

 

[pappus]

A circle of radius 8 in. is rotating 15^o/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 15^o/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 15^o to inches, can anyone help?

1. You don't specify the orientation of the axis of rotation. So I assume it passes through the center of the circle and is perpendicular to the plane where the circle is located.

2. I assume that you want to know the linear speed of a point on the circle line during rotation. That means you have to calculate the length of an arc corresponding to 1 s.
Let \(\displaystyle \alpha\) denotes the angle which is performed by a point of the circumference during 1 s of rotation. Then the length of the arc is:

\(\displaystyle a = \frac{\alpha}{360^\circ} \cdot 2 \pi r\)

3. Plug in the value for \(\displaystyle \alpha\) and r.

 

[Chaim]

1. You don't specify the orientation of the axis of rotation. So I assume it passes through the center of the circle and is perpendicular to the plane where the circle is located.

2. I assume that you want to know the linear speed of a point on the circle line during rotation. That means you have to calculate the length of an arc corresponding to 1 s.
Let \(\displaystyle \alpha\) denotes the angle which is performed by a point of the circumference during 1 s of rotation. Then the length of the arc is:

\(\displaystyle a = \frac{\alpha}{360^\circ} \cdot 2 \pi r\)

3. Plug in the value for \(\displaystyle \alpha\) and r.

Ooo I see, thanks!