A grinding wheel 0.40 m in diameter rotates at 2200 rpm.
What is the acceleration of a point on the edge of the grinding wheel?
centripetal acceleration= w^2 r
w = 2PI*2200r/min*1min/60sec
To find the acceleration of a point on the edge of the grinding wheel, we need to use the formula for linear acceleration:
acceleration = radius × (angular acceleration)
First, let's calculate the radius of the grinding wheel. The diameter is given as 0.40 m, so the radius would be half of that:
radius = 0.40 m / 2 = 0.20 m
Next, we need to convert the rotational speed from revolutions per minute (rpm) to radians per second (rad/s). We know that one revolution is equal to 2π radians, and there are 60 seconds in a minute. Therefore, the conversion factor is (2π rad) / (60 s).
rotational speed in radians per second = 2200 rpm × (2π rad) / (60 s)
= 2200 × 2π / 60 rad/s
≈ 230.39 rad/s
Now, we have the radius and the angular speed. To find the acceleration of a point on the edge of the grinding wheel, we multiply the radius by the square of the angular speed:
acceleration = 0.20 m × (230.39 rad/s)²
= 0.20 m × 53069.76 rad²/s²
≈ 10613.95 m/s²
Therefore, the acceleration of a point on the edge of the grinding wheel is approximately 10613.95 m/s².