Question

2. a) A disc rotates about its axis at speed 25 revolutions per minute and takes 15 s to stop. Calculate the

Answer 1

The statement shows a case of rotational motion, in which the disc decelerates at constant rate.

i) The angular acceleration of the disc ($\alpha$), in revolutions per square second, is found by the following kinematic formula:

$\alpha = \frac{\omega_{f}-\omega_{o}}{t}$ (1)

Where:

• $\omega_{o}$ - Initial angular speed, in revolutions per second.
• $\omega_{f}$ - Final angular speed, in revolutions per second.
• $t$ - Time, in seconds.

If we know that $\omega_{o} = \frac{5}{12}\,\frac{rev}{s}$, $\omega_{f} = 0\,\frac{rev}{s}$ y $t = 15\,s$, then the angular acceleration of the disc is:

$\alpha = \frac{0\,\frac{rev}{s}-\frac{5}{12}\,\frac{rev}{s}}{15\,s}$

$\alpha = -\frac{1}{36}\,\frac{rev}{s^{2}}$

The angular acceleration of the disc is $\frac{1}{36}$ radians per square second.

ii) The number of rotations that the disk makes before it stops ($\Delta \theta$), in revolutions, is determined by the following formula:

$\Delta \theta = \frac{\omega_{f}^{2}-\omega_{o}^{2}}{2\cdot \alpha}$ (2)

If we know that $\omega_{o} = \frac{5}{12}\,\frac{rev}{s}$, $\omega_{f} = 0\,\frac{rev}{s}$ y $\alpha = -\frac{1}{36}\,\frac{rev}{s^{2}}$, then the number of rotations done by the disc is:

$\Delta \theta = 3.125\,rev$

The disc makes 3.125 revolutions before it stops.

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