Question

A DVD with an initial angular speed of 4.0 rad/s accelerates at a rate of 2.0 rad/s2 , causing the DVD to slow down its rotation. What angular distance has the DVD rotated through before coming to rest?

Answer 1

Step-by-step explanation:

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Answer 2

4 rad =229º

Step-by-step explanation:

• If we assume that the angular acceleration is constant, we an find the angular distance rotated, using a kinematic equation very similar to the one used for linear displacement, as follows:

`\omega_(f) ^(2) -\omega_(0) ^(2) = 2* \alpha * \Delta \theta`

• As the DVD finally comes to rest, this means that ωf = 0.
• Replacing ω₀ and α by the respective givens, we can solve for Δθ, as follows:

`\Delta \theta = (\omega_(0) ^(2) )/(2*\alpha) = ((4rad/sec)^(2) )/(2*(2.0 rad/sec2)) = 4 rad`