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

The angular acceleration of the CD is -7.85 rad/s². The CD goes through approximately -96 revolutions.

Step-by-step explanation:

To find the angular acceleration of the CD, we need to use the formula:

Angular acceleration (α) = (Final angular velocity - Initial angular velocity) / time

Given that the initial angular velocity is 600 rpm and the time taken is 4 seconds:

Angular acceleration (α) = (0 - 600 rpm) / 4 s = -150 rpm/s

(a) The angular acceleration in rad/s² can be converted by multiplying by a conversion factor of 2π/60:

Angular acceleration (α) = (-150 rpm/s) x (2π/60 rad/s²) = -15π/6 rad/s² = -7.85 rad/s²

(b) To find the number of revolutions, we can use the formula:

Number of revolutions = (Final angular velocity - Initial angular velocity) / (2π)

Given that the final angular velocity is 0 rpm and the initial angular velocity is 600 rpm:

Number of revolutions = (0 - 600 rpm) / (2π)

Number of revolutions ≈ -96 revolutions (negative value indicates the CD is rotating in the opposite direction).

Answer 2

-15.708 rad/s^2

Step-by-step 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(rad)/(s)+\alpha *(4s)\\\alpha = -15.708(rad)/(s^2)`