A CD-ROM starts from rest and undergoes uniform angular acceleration until it reaches 26,000 rpm in 0.25 s.Through what angle does it rotate during this time?
A)54 rad
B)85 rad
C)340 rad
D)680 rad

Question

Quizplus · Accepted Answer

First, we need to convert the final angular velocity to radians per second:

26,000 rpm = 26,000/60 revolutions per second = 433.33... revolutions per second 
Each revolution is 2π radians, so:

433.33... revolutions per second x 2π radians/revolution = 2,725.6 radians per second

The angular acceleration can be found using the equation:

ωf = ωi + αt

Where ωi = 0 (starting from rest), ωf = 2,725.6 radians per second, t = 0.25 seconds, and solving for α:

α = (ωf - ωi)/t = 10,902.4 radians per second squared

Finally, we can use the equation for rotational displacement:

θ = ωit + (1/2)αt^2

Where ωi = 0, t = 0.25 seconds, and solving for θ:

θ = (1/2)αt^2 = 340 radians

Therefore, the answer is C, 340 rad.

A CD-ROM Starts from Rest and Undergoes Uniform Angular Acceleration