Angular/Linear Velocity

[dashaa]

A riding lawn mower wheels 15 in diameter turning at 2.5 revolutions per second.

The Angular Speed in radians per second is 15.71.

How do i use this information to find the Linear Speed in miles per hour ?

 

[mmm4444bot]

There's at least two approaches.

Each time the wheels revolve once, the mower moves forward a distance equal to the circumference of the wheel. You know this distance, and you know how much time it takes. Their ratio IS velocity: distance/time (in inches/second).

Or, you could just substitute values into the formula for linear velocity.

\(\displaystyle v = r \cdot \omega\)

where v is the linear velocity of a point on the circumference of the wheel, r is the radius, and ? is the angular velocity.

v = 15 * 15.71

Again, the units are inches per second. Convert to miles per hour.