A disk has a rotational inertia of 6.0 kg .m² and a constant angular acceleration of 2.0 rad/s². If it starts from rest the work done during the first 5.0 s by the net torque acting on it is: A) 0 B) 30 J C) 60 J D) 300 J E) 600 J

Question

Quizplus · Accepted Answer

The work done by a torque on a rotating object is given by:

$W = \frac{1}{2}I\omega^2$

where I is the rotational inertia of the object, $\omega$ is its angular velocity, and $W$ is the work done by the torque.

In this case, the disk starts from rest, so its initial angular velocity is 0. We are given that the disk has a rotational inertia of 6.0 kg·m$^2$ and a constant angular acceleration of 2.0 rad/s$^2$. We can use the following kinematic equation to find its angular velocity after 5 seconds:

$\omega = \omega_0 + \alpha t$

where $\omega_0$ is the initial angular velocity (0 in this case), $\alpha$ is the constant angular acceleration (2.0 rad/s$^2$), and t is the time (5.0 s in this case).

Plugging in these values, we get:

$\omega = 0 + (2.0	ext{ rad/s}^2)(5.0	ext{ s}) = 10.0	ext{ rad/s}$

Now we can use the equation for work to find the work done by the torque during the first 5 seconds:

$W = \frac{1}{2}I\omega^2 = \frac{1}{2}(6.0	ext{ kg·m}^2)(10.0	ext{ rad/s})^2 = 300	ext{ J}$

Therefore, the answer is D, 300 J.

A Disk Has a Rotational Inertia of 6