Question

Solve for (b) how many revolutions it takes for the cd to reach its maximum angular velocity in 1.36s?

Answer 1

Angular displacement of the cd is 3.25 rev

Explanation:

The question is incomplete. It is not given what is the maximum angular velocity of the cd.

Here we are going to assume that the maximum angular velocity is:

$\omega = 30 rad/s$

The motion of the cd is an accelerated angular motion, therefore we can use the following suvat equation:

$\theta = (\frac{\omega_0 + \omega}{2})t$

where:

$\theta$ is the angular displacement of the cd during the time interval t

$\omega_0$ is the initial angular velocity of the cd

$\omega$ is the final angular velocity

Here we have:

t = 1.36 s

$\omega_0 = 0$ (assuming the cd starts from rest)

Therefore, the angular displacement of the cd during this time is:

$\theta=(\frac{0+30}{2})(1.36)=20.4 rad$

And since $1 rev = 2 \pi rad$, we can convert into number of revolutions completed:

$\theta = 20.4 rad \cdot \frac{1}{2\pi rad/rev}=3.25 rev$

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