Final answer:
To calculate the kinetic energy of the disk after 4.40 s, we first find the angular acceleration from the applied force, then the angular velocity, and finally use these values to calculate the rotational kinetic energy.
Step-by-step explanation:
The student is asking about the kinetic energy of a rotating disk 4.40 seconds after a tangential force is applied. To solve this, we first need to calculate the angular acceleration (α) using the formula α = F * r / I, where F is the applied force, r is the radius of the disk, and I is the moment of inertia of the disk.
The moment of inertia of a solid disk is I = (1/2) * M * r^2, where M is the mass of the disk. Once we find α, we can find the angular velocity (ω) after 4.40 seconds using the equation ω = α * t, where t is time. Finally, the rotational kinetic energy (KErot) is given by KErot = (1/2) * I * ω^2.
Using the given values, the moment of inertia I = (1/2) * 19.0 kg * (3.2 m)^2, the angular acceleration α = 21.0 N * 3.2 m / I, and consequently, ω after 4.40 s is α * 4.40 s. The kinetic energy is then calculated using KErot = (1/2) * I * ω^2.