Angular Acceleration Homework: 962 Revolutions in 10 Secs

In summary, a computer disk starts from rest and reaches its final speed of 7200 rpm with an angular acceleration of 190 rad/s^2. After 10.0 seconds, it will have completed a total of 962 revolutions. This can be calculated using the equation φ=φ0+ω0t+1/2(α)t^2, where φ is the total revolutions, φ0 is the initial revolution, ω0 is the initial angular velocity, α is the angular acceleration, and t is the time.
  • #1
Wes Turner
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Homework Statement


A computer disk starts from rest, then speeds up with angular acceleration of 190 rad/s^2. until it reaches its final speed of 7200 rpm. How many revolutions will it have made 10.0 secs after starting up?

Homework Equations


w = w0 + at
rps = rpm / 60
1 rev = 2*pi rad
1 rad = 1/(2*pi) rev
190 rad/s^2 = (190/(2*pi)) rev/s^2 = 30.24 rev/s^2
7200 rpm = 7200/60 rps = 120 rps

The Attempt at a Solution


Calculate the time it will take to get up to full speed.
w = w0 + at
7200 rpm = 0 rpm + 190 rad/s^2 * t
120 rps = 0 rps + 30.24 rev/s^2 x t
t = 120 rev/s / 30.24 rev/s^2 = 3.97 s

Over the first 3.97 s, it the angular velocity increases linearly, so the average is 120 rps/2 = 60 rps.
At 60 rps for 3.97 sec, it completes 238 revolutions.

That leaves 10 s - 3.97 s = 6.03 s x 120 rps = 724 revolutions.

Then 238 + 723 = 962 total revolutions in the first 10 seconds.

Is that correct?

Thanks
 
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  • #2
Yes, correct solution. But instead of

Wes Turner said:
Over the first 3.97 s, it the angular velocity increases linearly, so the average is 120 rps/2 = 60 rps.

you could have calculated it with ##φ=\ddot{φ}\frac{t^2}{2}##.
 
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Related to Angular Acceleration Homework: 962 Revolutions in 10 Secs

1. What is angular acceleration?

Angular acceleration is a measure of how quickly an object's angular velocity changes over time. It is typically measured in radians per second squared (rad/s²).

2. How is angular acceleration different from linear acceleration?

Angular acceleration measures the rate of change of an object's angular velocity, while linear acceleration measures the rate of change of an object's linear velocity. Angular acceleration is a rotational motion, while linear acceleration is a straight-line motion.

3. How is angular acceleration calculated?

Angular acceleration can be calculated by dividing the change in angular velocity by the change in time. The formula is: angular acceleration = (final angular velocity - initial angular velocity) / time.

4. What does "962 revolutions in 10 seconds" mean in terms of angular acceleration?

This means that the object underwent 962 full rotations (revolutions) in a time period of 10 seconds. It also means that the object's angular acceleration was 962 revolutions per 10 seconds, or 96.2 revolutions per second squared (rev/s²).

5. How can I use angular acceleration in real-world applications?

Angular acceleration is used in various fields such as physics, engineering, and astronomy. It can be used to calculate the centripetal force in circular motion, analyze the stability of rotating objects, and predict the movements of celestial bodies. It is also important in designing and controlling machines that involve rotational motion, such as motors and turbines.

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