Question

The wheels on Darlene's car have on 11-inch radius. If the wheels are rotating at a rate of 378 rpm, find the linear speed in miles per hour in which she is traveling.

Answer 1

The linear speed in which Darlene is traveling is 24.74 miles per hour.

Explanation:

The wheel experiments rolling, which is a combination of translation and rotation. The point where linear speed happens is located at geometrical center of the wheel and instantaneous center of rotation is located at the point of contact between wheel and ground. The linear speed (
`v`), measured in inches per second, is defined by following expression:

`v = R\cdot \omega` (1)

Where:

`R` - Radius of the wheel, measured in inches.

`\omega` - Angular speed, measured in radians per second.

If we know that
`R = 11\,in` and
`\omega \approx 39.584\,(rad)/(s)`, then the linear speed, measured in miles per hour, in which Darlene is traveling is:

`v = 11\,in* (1\,mi)/(63360\,in) * 39.584\,(rad)/(s)* (3600\,s)/(h)`

`v \approx 24.74\,(mi)/(h)`

The linear speed in which Darlene is traveling is 24.74 miles per hour.