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question 13
problem reference 8 - 3
a wheel of diameter 40.0 cm starts from rest and rotates with a constant angular acceleration of 3.00 rad/s². the wheel completes two revolutions.
what is its angular displacement in radians?
0.318 rad
12.6 rad
6.28 rad
4.00 rad

Explanation:

Step1: Recall the conversion between revolutions and radians

One revolution is equal to \(2\pi\) radians. So, to find the angular displacement for \(n\) revolutions, we use the formula \(\Delta\theta = n\times2\pi\).

Step2: Substitute the number of revolutions

The wheel completes 2 revolutions. So, \(n = 2\). Substituting into the formula, we get \(\Delta\theta=2\times2\pi\) radians.

Step3: Calculate the value

We know that \(\pi\approx3.14\), so \(2\times2\pi = 4\pi\approx4\times3.14 = 12.56\approx12.6\) radians.

Answer:

12.6 rad (corresponding to the option with this value, e.g., if the options are as given, the answer is the option with "12.6 rad")