Question

A typical laser disc can spin as fast 1800 RPM. The angular speed is therefore 2pi* 1800/60=60 pi rad/s. If it takes 17s to stop the rotation from this top speed, how much change is in angle displacement (i.e. The change in angle measured in radians)? Report the result in absolute value.

Answer 1

Initial angular speed w = 1800 rev/min

                                 = 1800 (2xpi) rad / 60 s

                                 = 188.49 rad/s

Final angular speed w ' = 0

time t = 17 s

Angular accleration $\alpha$ = ( w ' - w ) / t

                                 = -11.087 rad/s ²

from the relation w ' ² - w ² = 2 $\alpha$ $\theta$

From this angular displacment $\theta$ = [w ' ² - w ² ] / 2 $\alpha$

                                                = 1602.11 rad