Question

A CD has an initial angular speed of 600 rpm. If the disc stop rotating after 4 seconds, what is its angular acceleration?

Answer 1

Answer:

-15.708 rad/s^2

Explanation:

First, let us covert everything to the same unit. For me, I find dealing with radians/sec more intuitive, but you can solve it in rpm. We are told that the initial angular speed is 600 rpm and after 4 seconds it stops. Let's convert 600 rpm into radians/sec. To do this, multiply by 2*pi/60. This gives 62.83 rad/s. Now let's review our info:

$\omega_i = 600rpm = 62.83rad/s\\\omega_f = 0\\t = 4s\\\alpha = ?$

Now we look up angular kinematics equations and the equation that has these parameters is

$\omega=\omega_0+\alpha t$

Substitute our values in:

$\omega=\omega_0+\alpha t\\0=62.83\frac{rad}{s}+\alpha *(4s)\\\alpha = -15.708\frac{rad}{s^2}$