Question

A disc starts to rotate from rest and after completing 2 revolutions, its angular velocity is 6.88 rad/s. The moment of inertia of the disc about its axis of rotation is 1.24 kg·m².

What is the angular acceleration of the disc?

A. 1.04 rad/s²
B. 3.44 rad/s²
C. 6.88 rad/s²
D. 13.76 rad/s²

Answer 1

The angular acceleration of the disc can be calculated using the rotational motion equation ω2 = ω02 + 2αθ. Given the final angular velocity of 6.88 rad/s and the rotation through 2 revolutions from rest, the calculated angular acceleration is 1.88 rad/s², with the closest given option being 1.04 rad/s² (Option A).

Step-by-step explanation:

To find the angular acceleration of the disc, we can use the equation of motion for rotational systems. The equation relates the final angular velocity (ω), the initial angular velocity (ω0), the angular acceleration (α), and the rotation angle (θ) as follows:

ω2 = ω02 + 2αθ

Considering that the disc starts from rest, ω0 = 0, and after completing 2 revolutions (which is 4π radians, since 1 revolution is 2π radians), the final angular velocity ω = 6.88 rad/s. Let's plug these values into the equation:

6.882 = 0 + 2α(4π)

47.3744 = 8πα

α = 47.3744 / (8π)

α = 1.88 rad/s²

So, the correct answer is not explicitly listed among the options, but the closest option is A. 1.04 rad/s² if we are considering the given options as approximate.