Physics
Physics
Problem
Inside a large cylindrical water tank, an inspection robot drives along the inner wall on wheels that do not slip. Starting from a painted reference line, the robot’s onboard sensor reports that its angular position about the tank’s central axis has changed by 2.00 rad when it has traveled 9.00 m along the wall. (a) Determine the interior radius of the tank. (b) The robot then travels an additional 75° along the wall. Calculate the extra linear distance it covers during this portion of the motion. (c) While completing the 75° portion, the robot maintains a constant angular speed of 0.50 rad s⁻¹. Calculate its linear speed for this interval.Intuitive explanation
The key is recognizing that arc length and angular displacement are linked through the radius of the circular path. When the robot travels along the tank's inner wall, it traces an arc, and the relationship connects the distance traveled (), the radius (), and the angle swept (). Since you know both the arc length and the angular change, you can rearrange to find the tank's radius—the missing piece that describes the geometry of the robot's path.
Intuitive explanation
The key is recognizing that arc length and angular displacement are linked through the radius of the circular path. When the robot travels along the tank's inner wall, it traces an arc, and the relationship connects the distance traveled (), the radius (), and the angle swept (). Since you know both the arc length and the angular change, you can rearrange to find the tank's radius—the missing piece that describes the geometry of the robot's path.