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

Question

Quizplus · Accepted Answer

The relationship between angular displacement (θ), angular velocity (ω), and angular acceleration (α) for a rotating object starting from rest is given by ω^2 = 2αθ. When the disk reaches an angular velocity ω, it has made 10 revolutions, which means θ = 10 revs. To double the angular velocity to 2ω, we use the same formula: (2ω)^2 = 4ω^2 = 2αθ'. Solving for θ' gives us θ' = 4θ = 4 * 10 revs = 40 revs in total. Since it already made 10 revolutions to reach ω, it needs an additional 30 revolutions to reach 2ω.

Starting from Rest,a Disk Rotates with Constant Angular Acceleration ω\omegaω ,Then How Many Additional Revolutions Are Required to Reach an Takes

Starting from Rest,a Disk Rotates with Constant Angular Acceleration $\omega$ ,Then How Many Additional Revolutions Are Required to Reach an Takes