A wheel having a moment of inertia of 5.00 kg ∙ m² starts from rest and accelerates under a constant torque of 3.00 N ∙ m for 8.00 s.What is the wheel's rotational kinetic energy at the end of 8.00 s?

Question

Quizplus · Accepted Answer

The rotational kinetic energy (KE_rot) of the wheel can be calculated using the formula KE_rot = 0.5 * I * ω^2, where I is the moment of inertia and ω is the angular velocity. First, we need to find the angular acceleration (α) using the torque (τ) and moment of inertia (I) with the formula τ = I * α, giving α = τ / I = 3.00 N∙m / 5.00 kg∙m^2 = 0.60 rad/s^2. Then, we find the angular velocity (ω) after 8.00 s using ω = α * t = 0.60 rad/s^2 * 8.00 s = 4.80 rad/s. Finally, KE_rot = 0.5 * 5.00 kg∙m^2 * (4.80 rad/s)^2 = 0.5 * 5.00 * 23.04 = 57.6 J.

A Wheel Having a Moment of Inertia of 5