Question

A wheel is rotating at 5 radians/sec, and the wheel has a 52-inch diameter. To the nearest foot per

minute, what is the velocity of a point on the rim?

Answer 1

650 feet/min

Explanation:

5 radians/sec is the angular velocity. To find the linear velocity, we need to multiply this velocity by the wheel radius, that is half of diameter, so it is 26 inches. So, we have 26*5=130 inches/sec. Converting to foot per minute, we need first to convert from inch to foot, and that is done multiplying by 0.08333, so we have 130*0.08333=10.833 foot/sec. Now, to convert from seconds to minutes, we multiply by 60, so 10.833*60 = 650 feet per minute.

Answer 2

`v = 650\,(ft)/(min)`

Explanation:

Linear speed of the wheel is given by the following formula:

`v = R\cdot \omega`

`v = (5\,(rad)/(s) )\cdot (26\,in)\cdot ((1\,ft)/(12\,in) )\cdot ((60\,sec)/(1\,min) )`

`v = 650\,(ft)/(min)`