If the rotational speed of a CD changes from 550 rpm to 200 rpm as it plays 30 minutes of music, what is the CD's average rotational acceleration?
To find the CD's average rotational acceleration, we need to determine the change in rotational speed (delta omega) and the time interval (delta t) over which this change occurs. Here's how you can calculate it:
1. Convert the given rotational speeds from rpm to radians per second:
- The initial speed of 550 rpm can be converted to radians per second by multiplying it by 2*pi/60. (1 revolution = 2*pi radians, and there are 60 seconds in a minute.)
- Similarly, the final speed of 200 rpm can be converted to radians per second by multiplying it by 2*pi/60.
For this problem, the initial speed, omega_i, will be (550 rpm) * (2*pi/60), and the final speed, omega_f, will be (200 rpm) * (2*pi/60).
2. Calculate the change in rotational speed (delta omega):
- This can be found by subtracting the initial speed (omega_i) from the final speed (omega_f). This will give you the change in speed over the given time period.
3. Determine the time interval (delta t):
- The problem states that the CD plays for 30 minutes. However, to calculate the average rotational acceleration, we need the time interval in seconds. So, you should convert 30 minutes to seconds by multiplying it by 60.
4. Calculate the average rotational acceleration (alpha_avg):
- This can be obtained by dividing the change in rotational speed (delta omega) by the time interval (delta t).
So, the formula for average rotational acceleration is:
alpha_avg = (omega_f - omega_i) / (delta t)
You can now plug in the values you calculated into this formula to find the average rotational acceleration of the CD.
To find the average rotational acceleration of the CD, we need to use the formula:
Average rotational acceleration = (final rotational speed - initial rotational speed) / time
Given:
Initial rotational speed = 550 rpm
Final rotational speed = 200 rpm
Time = 30 minutes = 30 * 60 = 1800 seconds
Substituting the values into the formula:
Average rotational acceleration = (200 rpm - 550 rpm) / 1800 seconds
Calculating the difference in rotational speed:
Average rotational acceleration = -350 rpm / 1800 seconds
To convert rpm (revolutions per minute) to rev/s (revolutions per second), we divide by 60:
Average rotational acceleration = -350 / (1800 * 60) rev/s
Simplifying the equation:
Average rotational acceleration = -0.00386 rev/s
Therefore, the CD's average rotational acceleration is approximately -0.00386 rev/s.
acceleration=(wf=wi)/time
= wondering waht units you want, I will do it in rad/sec^2
= (200*2PI-550*2PI)/(30*3600) s^2