Final answer:
The angular displacement of a ball that rolls forward a distance of 4m and has a radius of 0.25m is calculated using the formula s = rθ. Substituting the given values results in an angular displacement of 16 radians.
Step-by-step explanation:
The student has asked about the angular displacement of a ball given its radius and the linear distance it rolls forward without slipping. The angular displacement of a ball that rolls forward a distance of 4m and has a radius of 0.25m is calculated using the formula s = rθ. Substituting the given values results in an angular displacement of 16 radians.
To solve this problem, we use the relationship between linear displacement and angular displacement, which is given by the formula s = r\(θ), where s is the linear displacement, r is the radius of the ball, and \(θ) is the angular displacement in radians.
To calculate the angular displacement, rearrange the equation to \(θ = s/r). Substituting the given values, we get:
\(θ = 4m / 0.25m)
\(θ = 16 radians)
Therefore, the correct answer is b. 16rad.