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 J B)30 J C)60 J D)300 J E)600 J

Question

Quizplus · Accepted Answer

The formula to calculate work done by torque is:

Work = (1/2) * I * ω^2

Where I is the rotational inertia, ω is the angular velocity, and * represents multiplication.

As the disk starts from rest, the initial angular velocity is 0 rad/s. We are given that the disk has a constant angular acceleration of 2.0 rad/s^2. Using the formula,

ω = ω0 + αt

where ω0 is the initial angular velocity, α is the angular acceleration, and t is the time elapsed.

Plugging in the given values, we get:

ω = 0 + (2.0 rad/s^2) * (5.0 s) = 10.0 rad/s

Now, we can calculate the work done as:

Work = (1/2) * I * ω^2

Plugging in the given values, we get:

Work = (1/2) * (6.0 kg∙m^2) * (10.0 rad/s)^2 = 300 J

Therefore, the correct answer is D) 300 J.

A Disk Has a Rotational Inertia of 6