# Linear Speed/Rotational Speed

1. Feb 2, 2004

### celect

I can define both terms Linear Speed, Rotational speed,

but I need to find the formula difference so I can show how

rotational speed is changed to linear Speed.

I can not find the formula for either.

2. Feb 2, 2004

### Staff: Mentor

I assume you are talking about how to find the tangential speed (V) of something that is rotating about a point at some angular speed (&omega;, measured in radians/sec). The relationship is V=&omega;r, where r is the distance to the axis of rotation.

3. Feb 2, 2004

### HallsofIvy

Staff Emeritus
If the angular speed is &omega;, measured in radians per second, that means that in 1 second, the "wheel" will turn through &omega; radians. On a "wheel" of radius r, one radian angle cuts an arc of length r*1= r on the circumference of the wheel (remember that the full circle is 2&pi; radians and the entire circumference is 2&pi;r).
That is, in one second there is a revolution of &omega; radians which carries a point on the circumference a distance r&omega;.
Angular speed &omega; corresponds to a linear speed of v= r&omega;, just as Doc Al said.

4. Feb 3, 2004

### celect

Thanks to all.
I now understand
v=w*r
v= linear speed
w= Rotational Speed