Starting from rest, a disk rotates with constant angular acceleration. If it takes 10 rev to reach an angular velocity , then how many additional revolutions are required to reach an angular velocity 2?
A) 10 rev
B) 20 rev
C) 30 rev
D) 40 rev
E) 50 rev

Question

Quizplus · Accepted Answer

The angular displacement is proportional to the square of the angular velocity when starting from rest with constant angular acceleration. To double the angular velocity, the angular displacement must be four times the initial displacement (since (2ω)^2 = 4ω^2). Therefore, if it takes 10 revolutions to reach ω, it will take 40 revolutions to reach 2ω. Since 10 revolutions have already been completed, an additional 30 revolutions are needed.

Starting from Rest, a Disk Rotates with Constant Angular Acceleration