A floor polisher has a rotating disk that has a 17-cm radius. The disk rotates at a constant angular velocity of 1.3 rev/s and is covered with a soft material that does the polishing. An operator holds the polisher in one place for 50s, in order to buff an especially scuffed area of the floor. How far does a spot on the outer edge of the disk move during this time?
The formula to calculate the distance covered by a point on the edge of a rotating disk is:
distance = angular velocity * radius * time
Given:
radius = 17 cm
angular velocity = 1.3 rev/s
time = 50 s
Converting the radius to meters:
radius_m = 17 cm * 0.01 m/cm = 0.17 m
Calculating the distance covered:
distance = 1.3 rev/s * 0.17 m * 50 s = 110.5 m
Therefore, a spot on the outer edge of the disk moves approximately 110.5 meters during this time.