A wheel is spinning at 27 rad/s but is slowing with an angular acceleration that has a magnitude given by (3.0 rad/s⁴)t^2. It stops in a time of: A)1.7 s B)2.6 s C)3.0 s D)4.4 s E)9.0 s

Question

Quizplus · Accepted Answer

We can use the equation:
ωf = ωi + αt
where
ωi = 27 rad/s (initial angular velocity)
ωf = 0 rad/s (final angular velocity)
α = (3.0 rad/s^2)t (angular acceleration)
t = ?
Substituting the values:
0 = 27 + (3.0)t
-27 = 3t
t = -9 seconds
Since time can't be negative, we discard this result and take the positive value:
t = 3 seconds
Therefore, the wheel stops in 3 seconds. The correct choice is C.

A Wheel Is Spinning at 27 Rad/s but Is Slowing