To solve this problem, we first need to convert the measurements into standard units, since we are asked to find the linear speed in meters per second (m/s).
So, we start by converting the radius from centimeters to meters. Since 1 meter is equal to 100 centimeters, we get:
9.50 cm = 9.50 / 100 = 0.095 m
Next, we'll convert revolutions per minute (rpm) to revolutions per second as linear speed is standardly measured in meters per second. We know that there are 60 seconds in a minute, so we have:
6000 rpm = 6000 / 60 = 100 revolutions per second (rps).
Now that we have converted our units to the standard, we can start determining the linear speed.
Linear speed on the edge of a rotating body, such as the grindstone in this problem, is the product of the radius of the object and its angular speed. The angular speed is measured in radians per second. For a full revolution of 360 degrees, there are 2π radians. So, the angular speed is 2π multiplied by the number of revolutions per second.
Therefore, the angular speed = 2 * π * rps = 2 * π * 100 = 200π radians per second
And finally, we can calculate the linear speed by multiplying the radius we found in meters (0.095 m) by the angular speed in radians per second (200π rad/s). This gives us:
Linear speed = radius_m * angular speed = 0.095 m * 200π rad/s = 59.690260418206066 m/s.
So, the linear speed of a point on the edge of the grindstone is approximately 59.69 m/s.