The angular speed of digital video discs (DVDs) varies with whether the inner or outer part of the disc is being read. (CDs function in the same way.) Over a 133 min playing time, the angular speed varies from 570 rpm to 1600 rpm. Assuming it to be constant, what is the angular acceleration (in rad/s2) of such a DVD?

Question

The angular speed of digital video discs (DVDs) varies with whether the inner or outer part of the disc is being read. (CDs function in the same way.) Over a 133 min playing time, the angular speed varies from 570 rpm to 1600 rpm. Assuming it to be constant, what is the angular acceleration (in rad/s2) of such a DVD?

Answer 1

angular acceleration= (wf-wi)/timeinseconds

change rpm to rad/sec

570rpm*2PIrad/rev*1min/60sec.

Answer 2

To find the angular acceleration of the DVD, we need to calculate the change in angular speed over time.

Given:

Initial angular speed (ω1) = 570 rpm
Final angular speed (ω2) = 1600 rpm
Time (t) = 133 minutes = 133 * 60 = 7980 seconds

First, we need to convert the angular speeds from rpm to rad/s:

ω1 = 570 rpm * (2π rad/1 min) * (1 min/60 sec) = 60π rad/s
ω2 = 1600 rpm * (2π rad/1 min) * (1 min/60 sec) = 160π rad/s

Now, we can find the change in angular speed (Δω) as:

Δω = ω2 - ω1 = 160π rad/s - 60π rad/s = 100π rad/s

Next, we can find the angular acceleration (α) using the formula:

α = Δω / t

Plugging in the values:

α = (100π rad/s) / 7980 sec

Simplifying:

α ≈ 0.0125π rad/s²

Therefore, the angular acceleration of the DVD is approximately 0.0125π rad/s².

Answer 3

To find the angular acceleration of the DVD, we will need to convert the given angular speeds from rpm (revolutions per minute) to rad/s (radians per second), and then use the formula for angular acceleration.

Angular speed is defined as the rate at which an object rotates, measured in radians per unit of time. To convert from rpm to rad/s, we can use the following conversion factor:

1 revolution = 2π radians

1 minute = 60 seconds

Therefore, to convert from rpm to rad/s, we can multiply the given angular speed by the conversion factor (2π/60).

First, let's calculate the angular speeds at both ends of the DVD:

Angular speed at inner part = 570 rpm
Angular speed at outer part = 1600 rpm

Now, applying the conversion factor, we can find the angular speeds in rad/s:

Angular speed at inner part = 570 rpm * (2π/60) rad/s ≈ 60π rad/s
Angular speed at outer part = 1600 rpm * (2π/60) rad/s ≈ 160π rad/s

Next, we will use the formula for angular acceleration:

Angular acceleration = (final angular speed - initial angular speed) / time

Since the problem states that the angular speed is assumed to be constant over the playing time, the final angular speed is the same as the initial angular speed. Therefore, the angular acceleration will be zero.

Answer 4

so 570rpm*2pirad = 3581.415625

i divide that with rev*1min/60 sec == 59.69 is that correct ??