A floor polisher has a rotating disk that has a 19-cm radius. The disk rotates at a constant angular velocity of 1.6 rev/s and is covered with a soft material that does the polishing. An operator holds the polisher in one place for 43 s, in order to buff an especially scuffed area of the floor. How far (in meters) does a spot on the outer edge of the disk move during this time?

Question

Jester

Mathematics

14 August, 09:55

A floor polisher has a rotating disk that has a 19-cm radius. The disk rotates at a constant angular velocity of 1.6 rev/s and is covered with a soft material that does the polishing. An operator holds the polisher in one place for 43 s, in order to buff an especially scuffed area of the floor. How far (in meters) does a spot on the outer edge of the disk move during this time?

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Larissa Campbell · Answer 1

Answer: Arc length (S) = 82.14m

Step-by-step explanation:

Given: Radius=19cm = 0.19m, angular velocity = 1.6 rad/s, time = 43secs

As the disk is rotating, angular displacement=s/r

Where r=radius and s=arc length

The rate of change of the angular displacement represents the angular velocity. w=angular displacement / time

w = (1.6) (2*3.142)

w=10.054 rad/s

Angular displacement = at

Angular displacement = 10.054 * 43=432.32rad

S=angular displacement * radius

S = 432.32 * 0.19

S = 82.14m