A certain CD has a playing time of 80 minutes. When the music starts, the CD is rotating at an angular speed of 4.8 x 10^2 revolutions per minute (rpm). At the end of the music, the CD is rotating at 2.1 x 10^2 rpm. Find the magnitude of the average angular acceleration of the CD. Express your answer in rad/s2.
(0.104667 x -2.7) / (80 x 60)=
-0.000058875
[270 rev/min* 2 pi rad/rev* 1/60 min/sec]/(4800 sec) = 5.89*10^-3 rad/sec^2
You forgot the 10^2 multiplier on the rpms.
drwls the system is telling me the answer is incorrect. I saw where my I made the mistake and corrected it but it is still wrong. The answer I came up with is -0.00589 rad/sec^2.
You are right about the minus sign, since it is decelerating. Maybe they want you to use only two significant figures (-5.9*10^-3). Other than that, I don't see why it is getting marked wrong.
I had this prob with different numbers. it wants the answer in scientific notation. mine was 6.5E-3
To find the magnitude of the average angular acceleration of the CD, we can use the formula:
Average angular acceleration = (Final angular speed - Initial angular speed) / Time
The initial angular speed (ω1) is given as 4.8 x 10^2 revolutions per minute (rpm) and the final angular speed (ω2) is given as 2.1 x 10^2 rpm. We need to convert these values to radians per second (rad/s) as follows:
ω1 = (4.8 x 10^2) rpm
= (4.8 x 10^2) revolutions/minute
= (4.8 x 10^2) * (2π radians) / (1 minute) [since there are 2π radians in one revolution]
We can cancel out the "minute" unit and convert it to "seconds" by multiplying by 1/60:
= (4.8 x 10^2) * (2π radians) / (1 minute) * (1 minute/60 seconds)
= (4.8 x 10^2) * (2π radians) / (60 seconds)
= (4.8 x 2π) * 10^2 radians / 60 seconds
≈ 16π rad/s
Similarly, for ω2:
ω2 = (2.1 x 10^2) rpm
= (2.1 x 10^2) revolutions/minute
≈ 7π rad/s
Now, we can substitute these values into the formula for average angular acceleration:
Average angular acceleration = (Final angular speed - Initial angular speed) / Time
We are given the time as 80 minutes, but it should be converted to seconds:
Time = 80 minutes
= 80 * 60 seconds
= 4800 seconds
Therefore, the average angular acceleration is:
Average angular acceleration = (7π rad/s - 16π rad/s) / 4800 seconds
= -9π rad/s / 4800 seconds
≈ -0.0059 rad/s^2
So, the magnitude of the average angular acceleration of the CD is approximately 0.0059 rad/s^2 (or in rounded form, it can be written as -5.9 x 10^-3 rad/s^2), considering the negative sign indicates deceleration.