Final answer:
To find the angular displacement of the disk, we first calculate the angular velocity using the moment of inertia and the given angular momentum. We then multiply this velocity by the time duration to find the displacement. The disk undergoes an angular displacement of 30 radians in 3 seconds.
Step-by-step explanation:
The student's question involves calculating the angular displacement of a uniform disk given its radius, mass, and angular momentum. This falls within the concept of rotational motion in physics. To find the angular displacement (θ) in radians, we need to use the formula θ = ωt, where ω is the angular velocity and t is the time in seconds.
First, we find the angular velocity:
To calculate the angular velocity (ω), we can use the relationship L = Iω, where L is angular momentum and I is the moment of inertia for a uniform disk, given by I = ½MR² (where M is the mass of the disk and R is its radius).
We have the angular momentum (L = 0.4 kg m/s), mass (M = 2 kg), and radius (R = 0.2 m), so we can solve for ω as follows:
I = ½ × 2 kg × (0.2 m)² = 0.04 kg m²
ω = L / I = 0.4 kg m/s / 0.04 kg m² = 10 rad/s
With ω known, we multiply it by the time (t = 3 s) to find the angular displacement:
θ = ωt = 10 rad/s × 3 s = 30 radians
Therefore, the uniform disk undergoes an angular displacement of 30 radians in 3 seconds.