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What is the linear velocity in miles per hour of the tip of a 22-inch lawnmower blade spinning at 3000 revolutions per minute?

Answer :

Final answer:

The linear velocity of a 22-inch lawnmower blade spinning at 3000 rpm is approximately 59.1 mph. This is computed by converting the blade's length to miles and revolutions to hours then multiplying by 2π.

Explanation:

The subject question concerns the linear velocity of a spinning lawnmower blade. Specifically, a 22-inch blade spinning at 3000 revolutions per minute (rpm). To translate this rotational motion into linear velocity, we utilize the relationship between linear and rotational quantities. The linear velocity of a point in circular motion is given by the product of the radius and angular speed.

Firstly, convert the radius to miles, because the requested units are in miles per hour. The radius is half of the 22-inch diameter, and there are approximately 63,360 inches in one mile. Thus, the radius in miles is approximately 0.000173 miles.

Next, we convert revolutions per minute to revolutions per hour, because again the requested units are in miles per hour. One revolution is a complete circle, with the circumference being the entire path of one revolution. Convert 3000 rpm to revolutions per hour by multiplying by 60, resulting in 180,000 revolutions per hour.

Then, to calculate linear velocity, multiply the radius in miles by the angular speed in revolutions per hour and by 2π (since there are 2π radians in one circle), resulting in approximately 59.1 mph. Thus, the tip of the lawnmower blade moves at a linear velocity of approximately 59.1 miles per hour as it spins.

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