Final answer:
The angular momentum of the potter's disk at t=5s and t=10s is found by first calculating the angular acceleration, then the angular velocity at those times, and finally using the formula for angular momentum L=Iω. The correct answer is (c): at t=5s, 5.96 kg m²/s and at t=10s, 11.92 kg m²/s. Therefore, the correct answer is option c) (t=5s) 5.96 kg m²/s, (t=10s) 11.92 kg m²/s
Step-by-step explanation:
To find the angular momentum of a potter's disk spinning up, we can follow a few steps using physics principles. The disk spins up uniformly from 0 to 10 rev/s over 15 seconds, meaning it has a constant angular acceleration (denoted as α). We first calculate this angular acceleration using α = (ω_f - ω_i) / t, where ω_f is the final angular velocity, ω_i is the initial angular velocity (0 in this case because it starts from rest), and t is the time.
Angular acceleration (α) = (10 rev/s - 0 rev/s) / 15s = 0.67 rev/s².
Next, we need to find the angular velocity (ω) at t=5s and t=10s knowing the disk starts from rest (ω_i = 0). Angular velocity is found by ω = ω_i + αt. At t=5s, ω(5s) = 0 + (0.67 rev/s² * 5s), and at t=10s, ω(10s) = 0 + (0.67 rev/s² * 10s).
To convert rev/s to rad/s, we multiply by 2π as there are 2π radians in one revolution. Angular momentum (L) is given by L = Iω, where I is the moment of inertia for a solid disk which is I = 1/2 m r². The moment of inertia for our potter's disk is I = 1/2 (3 kg) (0.3 m)². With the moment of inertia and ω at the specific times, we can calculate L.
Angular momentum of the disk at:
- t=5s: L(5s) = Iω(5s)
- t=10s: L(10s) = Iω(10s)
Following the calculations, you can find that the correct answer to the problem is choice (c):
(t=5s) 5.96 kg m²/s
(t=10s) 11.92 kg m²/s
Therefore, the correct answer is option c) (t=5s) 5.96 kg m²/s, (t=10s) 11.92 kg m²/s