In: Physics
A rotating wheel requires 2.97-s to rotate through 37.0 revolutions. Its angular speed at the end of the 2.97-s interval is 97.0 rad/s. What is the constant angular acceleration of the wheel? _____ rad/s2
Time period = T = 2.97 sec
Number of revolutions = n = 37 rev
Angle through which the wheel rotated =
= 2
n
= 2
(37)
= 232.478
rad
Initial angular speed of the wheel = 1
Final angular speed of the wheel = 2 = 97
rad/s
Angular acceleration of the wheel =
2 =
1 +
T
1 =
2 -
T
=
1T +
T2/2
= (
2 -
T)T +
T2/2
=
2T -
T2 +
T2/2
=
2T -
T2/2
232.478 = (97)(2.97) - (2.97)2/2
= 12.61
rad/s2
Constant angular acceleration of the wheel = 12.61 rad/s2