# Starting from rest, a DVD steadily accelerates to 560 rpm in 1.0s, rotates at this angular speed for 3.0s, then steadily decelerates to a halt in 2.0s. How many revolutions does it make?

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Starting from rest, a DVD steadily accelerates to 560 rpm in 1.0s, rotates at this angular speed for 3.0s, then steadily decelerates to a halt in 2.0s. How many revolutions does it make?

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Step 1

Given information:

Initial angular velocity (ω0) = 0 rpm

Final angular velocity (ωf) = 560 rpm = 560 × (2π/60) = 58.64 rad/s

Time taken to reach final angular velocity (t) = 1 s

Let the angular acceleration = α1

Let no revolutions it makes while accelerating = θ1

Time for which it stays at that velocity = 3 s

Let the angular acceleration while deceleration be = α2

Time taken to come to rest from ω0 = 2 s

Step 2

From 1st equation of motion we can write:

Step 3

Given that the DVD rotates at that velocity for 3 sec, the angular displacement in this time be (θ2...

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