In order for a lawn mower blade to cut grass, it must strike the grass with a speed of at least 900 in/s. If the innermost part of the cutting edge is 6 in from the center of the blade, how many radians per second must the blade turn? How many revolutions per minute is this?

The lawn mower blade must turn at 1800 radians per second. The blade must turn at approximately 286.48 revolutions per minute to achieve a linear cutting edge speed of at least 900 in/s.

To determine how many radians per second the lawn mower blade must turn and how many revolutions per minute (rpm) this corresponds to, you can use the following information:

The linear speed of the blade's cutting edge should be at least 900 in/s.

The innermost part of the cutting edge is 6 inches from the center of the blade.

First, calculate the angular speed (in radians per second):

Angular Speed (ω) = Linear Speed (v) / Radius (r)

Where:

Linear Speed (v) = 900 in/s

Radius (r) = 6 inches

Convert the radius to feet (1 foot = 12 inches):

r = 6 inches / 12 = 0.5 feet

Now, calculate ω:

ω = 900 in/s / 0.5 feet = 1800 rad/s

So, the lawn mower blade must turn at 1800 radians per second.

To find the number of revolutions per minute (rpm), you can use the conversion:

1 revolution = 2π radians

ω (in rpm) = (ω (in rad/s)) / (2π)

ω (in rpm) = 1800 rad/s / (2π) ≈ 286.48 rpm

So, the blade must turn at approximately 286.48 revolutions per minute to achieve a linear cutting edge speed of at least 900 in/s.

To know more about speed

https://brainly.com/question/27888149

#SPJ4