A floor polisher has a rotating disk that has an 11-cm radius. The disk rotates at a constant angular velocity of 1.1 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

A floor polisher has a rotating disk that has an 11-cm radius. The disk rotates at a constant angular velocity of 1.1 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?

Answer 1

To find the distance that a spot on the outer edge of the disk moves during the given time, we need to use the formula:

Distance = Angular Velocity × Radius × Time

Given:
- Angular velocity (ω) = 1.1 rev/s
- Radius (r) = 11 cm

First, we need to convert the radius from centimeters to meters:
Radius (r) = 11 cm = 0.11 m (since 1 meter = 100 centimeters)

Next, we can calculate the distance moved by using the formula:
Distance = 1.1 rev/s × 0.11 m × 43 s

Now, let's calculate it:
Distance = 1.1 rev/s × 0.11 m × 43 s
Distance = 5.253 m

Therefore, during the 43 seconds, a spot on the outer edge of the disk will move approximately 5.253 meters.