) Joe has a playing time of 74 minutes. When the music starts, the CD rotating at an angular speed of 480 revolutions per minute (rpm). At the end of the music, the CD is rotating at 210 rpm. Find the magnitude of the average angular acceleration of the CD (in rad/s^2)
ang acceleration= (wf-wi)/time
change 74 min to seconds
change rpm to rad/sec (multiply by 2PI/60)
thanks a lot
To find the average angular acceleration of the CD, we need to use the formula:
Average angular acceleration = (final angular speed - initial angular speed) / time
Given:
Initial angular speed (ω1) = 480 rpm
Final angular speed (ω2) = 210 rpm
Time taken (t) = 74 minutes
First, let's convert the angular speeds from rpm to rad/s:
1 rev = 2π radians
1 minute = 60 seconds
ω1 = (480 rpm) * (2π radians/1 rev) * (1 minute/60 seconds)
= 480 * 2π/60 rad/s
= 480π/60 rad/s
= 8π rad/s
Similarly, ω2 = (210 rpm) * (2π radians/1 rev) * (1 minute/60 seconds)
= 210 * 2π/60 rad/s
= 7π rad/s
Now, let's convert the time from minutes to seconds:
t = 74 minutes * 60 seconds/1 minute
= 4440 seconds
Finally, we can calculate the average angular acceleration:
Average angular acceleration = (ω2 - ω1) / t
= (7π - 8π) / 4440
= -π / 4440
≈ -0.000708 rad/s^2
Therefore, the magnitude of the average angular acceleration of the CD is approximately 0.000708 rad/s^2.
To find the average angular acceleration of the CD, we need to first convert the angular speed from revolutions per minute (rpm) to radians per second (rad/s).
To convert from rpm to rad/s, we can use the conversion factor:
1 revolution = 2π radians
So, to convert from rpm to rad/s, we multiply the angular speed by 2π/60 since there are 60 seconds in a minute.
Let's convert the initial and final angular speeds:
Initial angular speed = 480 rpm
Initial angular speed in rad/s = 480 * (2π/60) = 480π/60 = 8π rad/s
Final angular speed = 210 rpm
Final angular speed in rad/s = 210 * (2π/60) = 210π/30 = 7π rad/s
Next, we can use the formula for average angular acceleration:
Average angular acceleration = (Change in angular speed) / (Change in time)
We already have the initial and final angular speeds. However, we need to find the change in time.
Given:
Playing time = 74 minutes
We need to convert the playing time from minutes to seconds since the angular speeds are given in rad/s.
Change in time = 74 minutes * 60 seconds/minute = 4440 seconds
Now we can calculate the average angular acceleration:
Average angular acceleration = (Final angular speed - Initial angular speed) / Change in time
= (7π - 8π) / 4440
= -π / 4440 rad/s^2
Therefore, the magnitude of the average angular acceleration of the CD is π / 4440 rad/s^2.