A certain CD has a playing time of 80 minutes. When the music starts, the CD is rotating at an angular speed of 4.8 102 revolutions per minute (rpm). At the end of the music, the CD is rotating at 2.1 102 rpm. Find the magnitude of the average angular acceleration of the CD. Express your answer in rad/s2.
avgangularacceleration= (wf-wi)/time
change rpm to rad/sec (rpm*2PI/60)
please tell me where i went wrong.
(2.1x10^2rpm - 4.8x10^2rpm)/ 80mins
(-270rpm)/ 80mins
change rpm to rad/sec
rpmx2(3.14)/60
(-270 rpm x 6.28)/ 60 = -28.26 rad/s
-28.26rad per sec / 80x60
av ang acc = -0.0058875
where you went wrong?
Looks right to me, except for the sig figures.
avg ang acc= (wf-wi)/t=2PI/60 *(2.1
E2-4.8E2)/80*60= 5.9E-3 rad/sec^2
It appears that you made a slight error in your calculation. Everything else seems correct. Let's go through the calculation again:
First, we need to convert the angular speeds from revolutions per minute (rpm) to radians per second (rad/s). We can do this by multiplying the angular speed by 2π/60.
Initial angular speed (wi) = 4.8 x 10^2 rpm x 2π/60 = 50.24 rad/s
Final angular speed (wf) = 2.1 x 10^2 rpm x 2π/60 = 21.99 rad/s
Next, we can calculate the average angular acceleration using the formula avgangularacceleration = (wf - wi) / time, where time is given as 80 minutes.
Average angular acceleration = (21.99 rad/s - 50.24 rad/s) / (80 minutes x 60 seconds/minute)
= -28.25 rad/s / (4800 seconds)
= -5.8854 x 10^-3 rad/s^2
The magnitude of the average angular acceleration is 5.8854 x 10^-3 rad/s^2, which is approximately 5.9 x 10^-3 rad/s^2 in scientific notation.