Rotational Velocity & Acceleration Video Lessons

Concept

# Problem: As you finish listening to your favorite compact disc (CD), the CD in the player slows down to a stop. Assume that the CD spins down with a constant angular acceleration. A) If the CD rotates clockwise (let's take clockwise rotation as positive) at 500rpm (revolutions per minute) while the last song is playing, and then spins down to zero angular speed in 2.60s with constant angular acceleration, what is alpha_vec, the angular acceleration of the CD, as it spins to a stop? B)How many revolutions does the CD make as it spins to a stop?

###### FREE Expert Solution

We'll use the equation:

$\overline{){{\mathbf{\omega }}}_{{\mathbf{f}}}{\mathbf{=}}{{\mathbf{\omega }}}_{{\mathbf{0}}}{\mathbf{+}}{\mathbf{\alpha }}{\mathbf{t}}}$

We'll also use the equation:

$\overline{){{{\mathbf{\omega }}}_{{\mathbf{f}}}}^{{\mathbf{2}}}{\mathbf{=}}{{{\mathbf{\omega }}}_{{\mathbf{0}}}}^{{\mathbf{2}}}{\mathbf{+}}{\mathbf{2}}{\mathbf{\alpha \theta }}}$

A)

Solve for α, from the first equation and get:

α = (ωf - ωt)/t

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###### Problem Details

As you finish listening to your favorite compact disc (CD), the CD in the player slows down to a stop. Assume that the CD spins down with a constant angular acceleration. A) If the CD rotates clockwise (let's take clockwise rotation as positive) at 500rpm (revolutions per minute) while the last song is playing, and then spins down to zero angular speed in 2.60s with constant angular acceleration, what is alpha_vec, the angular acceleration of the CD, as it spins to a stop? B)How many revolutions does the CD make as it spins to a stop?