A computer hard disk 8.0 cm in diameter is initially at rest. A small dot is pai

Question

A computer hard disk 8.0 cm in diameter is initially at rest. A small dot is painted on the edge of the disk. The disc accelerates at 690 rad/s^2 for 0.5 sec then coasts for another 0.5 sec. Part A what is the speed of the dot at 1 sec Part B Through how many revolutions has it turned A computer hard disk 8.0 cm in diameter is initially at rest. A small dot is painted on the edge of the disk. The disc accelerates at 690 rad/s^2 for 0.5 sec then coasts for another 0.5 sec. Part A what is the speed of the dot at 1 sec Part B Through how many revolutions has it turned Part B Through how many revolutions has it turned

Explanation / Answer

Angular velocity

wf = wi + a t = 0 + (690 * 0.50 s) = 345 rad/s

As the speed is constant after accelerating, speed

wf = 345 rad/s

v = r w = 0.08 * 345 = 27.6 m/s

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Angular distance

theta' = 0 + 0.5 * 690 * 0.52 = 86.25 rad

Angular distance at constant speed theta'' = v t = 345 * 0.50 = 172.5 rad

distance = theta' + theta'' = 258.75 rad

258.75 rad = 41.2 rev

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