What is the Formula for Converting Rotational Speed to Linear Speed?

In summary, the formula for finding tangential speed (V) of something rotating at an angular speed (ω) is V=ωr, where r is the distance to the axis of rotation. This means that in one second, the "wheel" will turn through ω radians, which corresponds to a linear speed of v= rω. The full formula is v=w*r, where v is the linear speed, w is the rotational speed, and r is the radius.
  • #1
celect
43
0
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.
 
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  • #2
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 (ω, measured in radians/sec). The relationship is V=ωr, where r is the distance to the axis of rotation.
 
  • #3
If the angular speed is ω, measured in radians per second, that means that in 1 second, the "wheel" will turn through ω 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 2π radians and the entire circumference is 2πr).
That is, in one second there is a revolution of ω radians which carries a point on the circumference a distance rω.
Angular speed ω corresponds to a linear speed of v= rω, just as Doc Al said.
 
  • #4
Thanks to all.
I now understand
v=w*r
v= linear speed
w= Rotational Speed
r=radius
 

1. What is linear speed?

Linear speed, also known as tangential speed, is the distance traveled by an object in a given amount of time along a straight path. It is typically measured in meters per second (m/s).

2. How is linear speed different from rotational speed?

Linear speed refers to the speed of an object moving in a straight line, while rotational speed refers to the speed of an object spinning or rotating around an axis. Rotational speed is typically measured in rotations per minute (RPM) or radians per second (rad/s).

3. What factors affect linear speed?

The factors that affect linear speed include the distance traveled, the time taken to travel that distance, and the acceleration of the object. Other factors such as friction, air resistance, and the object's mass can also impact its linear speed.

4. How is rotational speed calculated?

Rotational speed can be calculated by dividing the total number of rotations or revolutions by the time taken to complete those rotations. For example, if an object completes 10 rotations in 5 seconds, its rotational speed would be 10/5 = 2 rotations per second.

5. Can linear speed and rotational speed be converted into each other?

Yes, linear speed and rotational speed can be converted into each other using the formula: linear speed = rotational speed x radius. This means that as the radius of an object increases, its linear speed will also increase for the same rotational speed, and vice versa.

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